Open in CoCalc
#### Group 5 Lab 4 Grade: 20/20. Good job!!
def iterate(fcn,num_times,initial):
count=srange(0,num_times)
vals=[initial]
for i in count:
b=fcn(vals[i])
vals.append(b)
return vals

var("N")
h=0.1
g(N)=N+h*0.2*N*(1-N/100)
count=int(round(100/h))
L= iterate(g,count,10)

N
#Value of N at 100 is L[1000]
list_plot(L,plotjoined=True)
L[1000]
##### Good. -HK

99.9999984129133


N
var("N")
h=0.1
g(N)=N+h*0.2*N*(1-N/100)
count=int(round(100/h))
Ex2= iterate(g,count,20)

N
var("N")
h=0.1
g(N)=N+h*0.2*N*(1-N/100)
count=int(round(100/h))
Ex2a= iterate(g,count,150)

N
Ex2a

#Exercise 3

def iterate(fcn,num_times,initial):
count=srange(0,num_times)
vals=[initial]
for i in count:
b=fcn(vals[i])
vals.append(b)
return vals

var("N")
h=0.1
g(N)=N+h*0.2*N*(1-N/100)
count=int(round(100/h))
L= iterate(g,count,10)
L[100]

tfinal=srange(0,100+h,h)
list_plot(zip(tfinal, L)) ##### Good. -HK

[150, 148.500000000000, 147.059550000000, 145.675438750759, 144.344680834729, 143.064497074368, 141.832296951227, 140.645662798559, 139.502335561721, 138.400201947521, 137.337282806648, 136.311722613039, 135.321779920953, 134.365818695177, 133.442300422355, 132.549776922400, 131.686883788413, 130.852334391800, 130.044914396480, 129.263476732332, 128.506936983592, 127.774269152683, 127.064501764236, 126.376714277802, 125.710033781028, 125.063631938003, 124.436722170058, 123.828557048574, 123.238425881399, 122.665652476282, 122.109593066321, 121.569634383883, 121.045191870714, 120.535708013125, 120.040650792142, 119.559512239465, 119.091807090867, 118.637071529450, 118.194862011823, 117.764754170860, 117.346341789293, 116.939235838813, 116.543063579876, 116.157467717757, 115.782105610792, 115.416648527074, 115.060780946171, 114.714199902706, 114.376614368896, 114.047744673376, 113.727321953827, 113.415087641145, 113.110792973039, 112.814198535101, 112.525073827580, 112.243196856151, 111.968353745176, 111.700338371999, 111.438952020955, 111.184003055868, 110.935306609880, 110.692684291552, 110.455963906249, 110.224979191883, 109.999569568150, 109.779579898478, 109.564860263910, 109.355265748258, 109.150656233849, 108.950896207270, 108.755854574542, 108.565404485185, 108.379423164682, 108.197791754874, 108.020395161845, 107.847121910898, 107.677864008223, 107.512516808913, 107.350978890974, 107.193151935023, 107.038940609371, 106.888252460203, 106.740997806608, 106.597089640190, 106.456443529042, 106.318977525852, 106.184612079941, 106.053269953026, 105.924876138541, 105.799357784318, 105.676644118490, 105.556666378431, 105.439357742614, 105.324653265231, 105.212489813447, 105.102806007167, 104.995542161195, 104.890640229674, 104.788043752709, 104.687697805059, 104.589548946816, 104.493545175973, 104.399635882803, 104.307771805967, 104.217904990261, 104.129988745955, 104.043977609627, 103.959827306453, 103.877494713865, 103.796937826536, 103.718115722634, 103.640988531276, 103.565517401153, 103.491664470263, 103.419392836703, 103.348666530494, 103.279450486378, 103.211710517552, 103.145413290311, 103.080526299552, 103.017017845104, 102.954857008867, 102.894013632701, 102.834458297065, 102.776162300356, 102.719097638926, 102.663236987753, 102.608553681748, 102.555021697651, 102.502615636522, 102.451310706787, 102.401082707815, 102.351908014025, 102.303763559483, 102.256626822986, 102.210475813602, 102.165289056666, 102.121045580193, 102.077724901718, 102.035307015531, 101.993772380290, 101.953101907024, 101.913276947471, 101.874279282786, 101.836091112565, 101.798695044199, 101.762074082542, 101.726211619877, 101.691091426168, 101.656697639602, 101.623014757397, 101.590027626868, 101.557721436760, 101.526081708810, 101.495094289557, 101.464745342379, 101.435021339748, 101.405909055704, 101.377395558535, 101.349468203660, 101.322114626700, 101.295322736749, 101.269080709815, 101.243376982449, 101.218200245536, 101.193539438258, 101.169383742215, 101.145722575703, 101.122545588145, 101.099842654662, 101.077603870796, 101.055819547360, 101.034480205429, 101.013576571462, 100.993099572539, 100.973040331736, 100.953390163604, 100.934140569771, 100.915283234655, 100.896810021282, 100.878712967213, 100.860984280573, 100.843616336176, 100.826601671747, 100.809932984248, 100.793603126275, 100.777605102565, 100.761932066575, 100.746577317148, 100.731534295267, 100.716796580877, 100.702357889792, 100.688212070675, 100.674353102090, 100.660775089627, 100.647472263091, 100.634438973763, 100.621669691725, 100.609159003250, 100.596901608247, 100.584892317776, 100.573126051615, 100.561597835889, 100.550302800745, 100.539236178096, 100.528393299403, 100.517769593519, 100.507360584578, 100.497161889934, 100.487169218146, 100.477378367014, 100.467785221653, 100.458385752617, 100.449176014065, 100.440152141965, 100.431310352344, 100.422646939574, 100.414158274695, 100.405840803786, 100.397691046358, 100.389705593798, 100.381881107832, 100.374214319039, 100.366702025387, 100.359341090804, 100.352128443784, 100.345061076020, 100.338136041071, 100.331350453053, 100.324701485367, 100.318186369449, 100.311802393547, 100.305546901529, 100.299417291717, 100.293411015740, 100.287525577420, 100.281758531680, 100.276107483472, 100.270570086734, 100.265144043365, 100.259827102225, 100.254617058156, 100.249511751024, 100.244509064781, 100.239606926548, 100.234803305722, 100.230096213089, 100.225483699973, 100.220963857394, 100.216534815241, 100.212194741471, 100.207941841320, 100.203774356532, 100.199690564603, 100.195688778047, 100.191767343666, 100.187924641850, 100.184159085879, 100.180469121248, 100.176853225002, 100.173309905089, 100.169837699723, 100.166435176760, 100.163100933091, 100.159833594046, 100.156631812810, 100.153494269848, 100.150419672353, 100.147406753691, 100.144454272867, 100.141561014002, 100.138725785818, 100.135947421133, 100.133224776370, 100.130556731074, 100.127942187441, 100.125380069851, 100.122869324422, 100.120408918559, 100.117997840526, 100.115635099018, 100.113319722742, 100.111050760016, 100.108827278361, 100.106648364118, 100.104513122061, 100.102420675022, 100.100370163522, 100.098360745418, 100.096391595542, 100.094461905363, 100.092570882646, 100.090717751119, 100.088901750155, 100.087122134447, 100.085378173705, 100.083669152345, 100.081994369192, 100.080353137193, 100.078744783124, 100.077168647313, 100.075624083367, 100.074110457899, 100.072627150269, 100.071173552323, 100.069749068142, 100.068353113793, 100.066985117087, 100.065644517344, 100.064330765157, 100.063043322164, 100.061781660829, 100.060545264218, 100.059333625787, 100.058146249176, 100.056982647995, 100.055842345631, 100.054724875045, 100.053629778581, 100.052556607779, 100.051504923184, 100.050474294169, 100.049464298755, 100.048474523436, 100.047504563012, 100.046554020415, 100.045622506551, 100.044709640137, 100.043815047544, 100.042938362642, 100.042079226648, 100.041237287983, 100.040412202121, 100.039603631449, 100.038811245130, 100.038034718965, 100.037273735258, 100.036527982687, 100.035797156174, 100.035080956763, 100.034379091493, 100.033691273279, 100.033017220793, 100.032356658350, 100.031709315792, 100.031074928380, 100.030453236682, 100.029843986469, 100.029246928607, 100.028661818958, 100.028088418279, 100.027526492122, 100.026975810738, 100.026436148984, 100.025907286230, 100.025389006268, 100.024881097222, 100.024383351464, 100.023895565525, 100.023417540015, 100.022949079539, 100.022489992616, 100.022040091604, 100.021599192618, 100.021167115461, 100.020743683542, 100.020328723811, 100.019922066684, 100.019523545972, 100.019132998819, 100.018750265628, 100.018375190001, 100.018007618672, 100.017647401444, 100.017294391129, 100.016948443487, 100.016609417167, 100.016277173649, 100.015951577187, 100.015632494753, 100.015319795983, 100.015013353124, 100.014713040981, 100.014418736867, 100.014130320549, 100.013847674205, 100.013570682370, 100.013299231889, 100.013033211878, 100.012772513667, 100.012517030767, 100.012266658816, 100.012021295545, 100.011780840732, 100.011545196160, 100.011314265578, 100.011087954664, 100.010866170983, 100.010648823948, 100.010435824790, 100.010227086513, 100.010022523864, 100.009822053296, 100.009625592936, 100.009433062547, 100.009244383499, 100.009059478737, 100.008878272748, 100.008700691528, 100.008526662557, 100.008356114765, 100.008188978505, 100.008025185523, 100.007864668932, 100.007707363183, 100.007553204038, 100.007402128547, 100.007254075018, 100.007108982993, 100.006966793226, 100.006827447654, 100.006690889378, 100.006557062637, 100.006425912785, 100.006297386271, 100.006171430614, 100.006047994385, 100.005927027181, 100.005808479612, 100.005692303272, 100.005578450726, 100.005466875488, 100.005357532001, 100.005250375620, 100.005145362594, 100.005042450047, 100.004941595961, 100.004842759158, 100.004745899285, 100.004650976794, 100.004557952932, 100.004466789718, 100.004377449933, 100.004289897102, 100.004204095480, 100.004120010035, 100.004037606440, 100.003956851050, 100.003877710898, 100.003800153673, 100.003724147711, 100.003649661983, 100.003576666079, 100.003505130199, 100.003435025138, 100.003366322275, 100.003298993563, 100.003233011516, 100.003168349195, 100.003104980203, 100.003042878671, 100.002982019246, 100.002922377082, 100.002863927833, 100.002806647635, 100.002750513107, 100.002695501332, 100.002641589852, 100.002588756660, 100.002536980186, 100.002486239295, 100.002436513273, 100.002387781820, 100.002340025044, 100.002293223447, 100.002247357927, 100.002202409758, 100.002158360593, 100.002115192449, 100.002072887705, 100.002031429092, 100.001990799685, 100.001950982898, 100.001911962479, 100.001873722499, 100.001836247346, 100.001799521725, 100.001763530643, 100.001728259408, 100.001693693623, 100.001659819176, 100.001626622242, 100.001594089268, 100.001562206974, 100.001530962347, 100.001500342631, 100.001470335328, 100.001440928189, 100.001412109210, 100.001383866627, 100.001356188912, 100.001329064765, 100.001302483117, 100.001276433115, 100.001250904127, 100.001225885732, 100.001201367716, 100.001177340073, 100.001153792995, 100.001130716869, 100.001108102276, 100.001085939984, 100.001064220949, 100.001042936303, 100.001022077360, 100.001001635604, 100.000981602691, 100.000961970444, 100.000942730850, 100.000923876056, 100.000905398364, 100.000887290233, 100.000869544271, 100.000852153234, 100.000835110024, 100.000818407684, 100.000802039396, 100.000785998480, 100.000770278387, 100.000754872700, 100.000739775132, 100.000724979520, 100.000710479825, 100.000696270127, 100.000682344628, 100.000668697642, 100.000655323600, 100.000642217042, 100.000629372619, 100.000616785087, 100.000604449309, 100.000592360250, 100.000580512975, 100.000568902648, 100.000557524530, 100.000546373977, 100.000535446438, 100.000524737452, 100.000514242648, 100.000503957742, 100.000493878536, 100.000484000917, 100.000474320852, 100.000464834390, 100.000455537659, 100.000446426864, 100.000437498287, 100.000428748283, 100.000420173280, 100.000411769779, 100.000403534350, 100.000395463630, 100.000387554327, 100.000379803210, 100.000372207117, 100.000364762947, 100.000357467661, 100.000350318282, 100.000343311892, 100.000336445631, 100.000329716696, 100.000323122340, 100.000316659872, 100.000310326655, 100.000304120102, 100.000298037682, 100.000292076910, 100.000286235355, 100.000280510632, 100.000274900403, 100.000269402380, 100.000264014318, 100.000258734018, 100.000253559324, 100.000248488125, 100.000243518350, 100.000238647971, 100.000233875000, 100.000229197489, 100.000224613529, 100.000220121248, 100.000215718814, 100.000211404428, 100.000207176331, 100.000203032795, 100.000198972131, 100.000194992681, 100.000191092819, 100.000187270956, 100.000183525530, 100.000179855012, 100.000176257906, 100.000172732741, 100.000169278080, 100.000165892513, 100.000162574657, 100.000159323159, 100.000156136691, 100.000153013952, 100.000149953668, 100.000146954590, 100.000144015494, 100.000141135180, 100.000138312473, 100.000135546219, 100.000132835291, 100.000130178582, 100.000127575007, 100.000125023504, 100.000122523030, 100.000120072567, 100.000117671113, 100.000115317687, 100.000113011331, 100.000110751102, 100.000108536077, 100.000106365354, 100.000104238044, 100.000102153281, 100.000100110213, 100.000098108007, 100.000096145845, 100.000094222926, 100.000092338466, 100.000090491695, 100.000088681859, 100.000086908221, 100.000085170055, 100.000083466652, 100.000081797318, 100.000080161370, 100.000078558141, 100.000076986977, 100.000075447237, 100.000073938291, 100.000072459524, 100.000071010332, 100.000069590125, 100.000068198321, 100.000066834354, 100.000065497666, 100.000064187712, 100.000062903957, 100.000061645877, 100.000060412958, 100.000059204699, 100.000058020604, 100.000056860191, 100.000055722987, 100.000054608526, 100.000053516355, 100.000052446027, 100.000051397106, 100.000050369164, 100.000049361780, 100.000048374544, 100.000047407052, 100.000046458911, 100.000045529732, 100.000044619137, 100.000043726754, 100.000042852219, 100.000041995174, 100.000041155270, 100.000040332164, 100.000039525521, 100.000038735010, 100.000037960310, 100.000037201103, 100.000036457081, 100.000035727939, 100.000035013380, 100.000034313112, 100.000033626849, 100.000032954312, 100.000032295226, 100.000031649321, 100.000031016334, 100.000030396008, 100.000029788087, 100.000029192325, 100.000028608479, 100.000028036309, 100.000027475583, 100.000026926071, 100.000026387549, 100.000025859798, 100.000025342602, 100.000024835750, 100.000024339035, 100.000023852254, 100.000023375209, 100.000022907704, 100.000022449550, 100.000022000559, 100.000021560548, 100.000021129337, 100.000020706750, 100.000020292615, 100.000019886763, 100.000019489027, 100.000019099247, 100.000018717262, 100.000018342916, 100.000017976058, 100.000017616537, 100.000017264206, 100.000016918922, 100.000016580543, 100.000016248932, 100.000015923954, 100.000015605474, 100.000015293365, 100.000014987498, 100.000014687748, 100.000014393993, 100.000014106113, 100.000013823990, 100.000013547511, 100.000013276560, 100.000013011029, 100.000012750808, 100.000012495792, 100.000012245876, 100.000012000959, 100.000011760940, 100.000011525721, 100.000011295206, 100.000011069302, 100.000010847916, 100.000010630958, 100.000010418339, 100.000010209972, 100.000010005772, 100.000009805657, 100.000009609544, 100.000009417353, 100.000009229006, 100.000009044426, 100.000008863537, 100.000008686266, 100.000008512541, 100.000008342290, 100.000008175444, 100.000008011935, 100.000007851697, 100.000007694663, 100.000007540769, 100.000007389954, 100.000007242155, 100.000007097312, 100.000006955366, 100.000006816258, 100.000006679933, 100.000006546334, 100.000006415408, 100.000006287100, 100.000006161358, 100.000006038130, 100.000005917368, 100.000005799020, 100.000005683040, 100.000005569379, 100.000005457992, 100.000005348832, 100.000005241855, 100.000005137018, 100.000005034278, 100.000004933592, 100.000004834920, 100.000004738222, 100.000004643457, 100.000004550588, 100.000004459576, 100.000004370385, 100.000004282977, 100.000004197318, 100.000004113371, 100.000004031104, 100.000003950482, 100.000003871472, 100.000003794043, 100.000003718162, 100.000003643799, 100.000003570923, 100.000003499504, 100.000003429514, 100.000003360924, 100.000003293705, 100.000003227831, 100.000003163275, 100.000003100009, 100.000003038009, 100.000002977249, 100.000002917704, 100.000002859350, 100.000002802163, 100.000002746119, 100.000002691197, 100.000002637373, 100.000002584626, 100.000002532933, 100.000002482274, 100.000002432629, 100.000002383976, 100.000002336297, 100.000002289571, 100.000002243779, 100.000002198904, 100.000002154926, 100.000002111827, 100.000002069591, 100.000002028199, 100.000001987635, 100.000001947882, 100.000001908925, 100.000001870746, 100.000001833331, 100.000001796665, 100.000001760731, 100.000001725517, 100.000001691006, 100.000001657186, 100.000001624042, 100.000001591562, 100.000001559730, 100.000001528536, 100.000001497965, 100.000001468006, 100.000001438646, 100.000001409873, 100.000001381675, 100.000001354042, 100.000001326961, 100.000001300422, 100.000001274413, 100.000001248925, 100.000001223947, 100.000001199468, 100.000001175478, 100.000001151969, 100.000001128929, 100.000001106351, 100.000001084224, 100.000001062539, 100.000001041288, 100.000001020463, 100.000001000053, 100.000000980052, 100.000000960451, 100.000000941242, 100.000000922417, 100.000000903969, 100.000000885890, 100.000000868172, 100.000000850808, 100.000000833792, 100.000000817116, 100.000000800774, 100.000000784759, 100.000000769063, 100.000000753682, 100.000000738609, 100.000000723836, 100.000000709360, 100.000000695172, 100.000000681269, 100.000000667644, 100.000000654291, 100.000000641205, 100.000000628381, 100.000000615813, 100.000000603497, 100.000000591427, 100.000000579598, 100.000000568007, 100.000000556646, 100.000000545513, 100.000000534603, 100.000000523911, 100.000000513433, 100.000000503164, 100.000000493101, 100.000000483239, 100.000000473574, 100.000000464103, 100.000000454821, 100.000000445724, 100.000000436810, 100.000000428074, 100.000000419512, 100.000000411122, 100.000000402899, 100.000000394841, 100.000000386945, 100.000000379206, 100.000000371622, 100.000000364189, 100.000000356905, 100.000000349767, 100.000000342772, 100.000000335916, 100.000000329198, 100.000000322614, 100.000000316162, 100.000000309839, 100.000000303642, 100.000000297569, 100.000000291618, 100.000000285785, 100.000000280070, 100.000000274468, 100.000000268979, 100.000000263599, 100.000000258327, 100.000000253161, 100.000000248098, 100.000000243136, 100.000000238273, 100.000000233507, 100.000000228837, 100.000000224261, 100.000000219775, 100.000000215380, 100.000000211072, 100.000000206851, 100.000000202714, 100.000000198659, 100.000000194686, 100.000000190793, 100.000000186977, 100.000000183237, 100.000000179572, 100.000000175981, 100.000000172461, 100.000000169012, 100.000000165632, 100.000000162319, 100.000000159073, 100.000000155891, 100.000000152774, 100.000000149718, 100.000000146724, 100.000000143789, 100.000000140913, 100.000000138095, 100.000000135333, 100.000000132627, 100.000000129974, 100.000000127375, 100.000000124827, 100.000000122331, 100.000000119884, 100.000000117486, 100.000000115137, 100.000000112834, 100.000000110577, 100.000000108366, 100.000000106198, 100.000000104074, 100.000000101993, 100.000000099953, 100.000000097954, 100.000000095995, 100.000000094075, 100.000000092193, 100.000000090350, 100.000000088543, 100.000000086772, 100.000000085036, 100.000000083336, 100.000000081669, 100.000000080035, 100.000000078435, 100.000000076866, 100.000000075329, 100.000000073822, 100.000000072346, 100.000000070899, 100.000000069481, 100.000000068091, 100.000000066729, 100.000000065395, 100.000000064087, 100.000000062805, 100.000000061549, 100.000000060318, 100.000000059112, 100.000000057930, 100.000000056771, 100.000000055635] N 44.8350628385566
#It comes up with an error if zip is not used

#Exercise 4
def iterate(fcn,num_times,initial):
count=srange(0,num_times)
vals=[initial]
for i in count:
b=fcn(vals[i])
vals.append(b)
return vals

def euler1(diff_eq, initial, h, num_times):
fcn(N)=N+h*diff_eq(N)
ex4out=iterate(fcn, num_times, initial)
return ex4out

N_prime(N)=0.2*N*(1-N/100)
h=0.1
out4=euler1(N_prime, 10, h, 1000)

out4

[10, 10.1800000000000, 10.3628735200000, 10.5486531608817, 10.7373714073976, 10.9290606065975, 11.1237529455809, 11.3214804285737, 11.5222748533262, 11.7261677868336, 11.9331905403773, 12.1433741438903, 12.3567493196484, 12.5733464552916, 12.7931955761805, 13.0163263170940, 13.2427678932773, 13.4725490708478, 13.7056981365714, 13.9422428670207, 14.1822104971285, 14.4256276881541, 14.6725204950778, 14.9229143334436, 15.1768339456718, 15.4343033668624, 15.6953458901155, 15.9599840313958, 16.2282394939672, 16.5001331324319, 16.7756849164029, 17.0549138938481, 17.3378381541397, 17.6244747908507, 17.9148398643370, 18.2089483641508, 18.5068141713282, 18.8084500206003, 19.1138674625768, 19.4230768259530, 19.7360871797947, 20.0529062959569, 20.3735406116931, 20.6979951925157, 21.0262736953681, 21.3583783321730, 21.6943098338204, 22.0340674146637, 22.3776487375901, 22.7250498797374, 23.0762652989248, 23.4312878008740, 23.7901085072900, 24.1527168248781, 24.5191004153711, 24.8892451666427, 25.2631351649825, 25.6407526686093, 26.0220780824990, 26.4070899346026, 26.7957648535318, 27.1880775477853, 27.5840007865921, 27.9835053824450, 28.3865601753961, 28.7931320191857, 29.2031857692746, 29.6166842728451, 30.0335883608386, 30.4538568420897, 30.8774464996198, 31.3043120891448, 31.7344063398528, 32.1676799575012, 32.6040816298816, 33.0435580346936, 33.4860538498691, 33.9315117663792, 34.3798725035564, 34.8310748269554, 35.2850555687743, 35.7417496508515, 36.2010901102477, 36.6630081274186, 37.1274330569767, 37.5942924610362, 38.0635121451277, 38.5350161966658, 39.0087270259437, 39.4845654096256, 39.9624505367008, 40.4423000568551, 40.9240301312145, 41.4075554854027, 41.8927894648554, 42.3796440923231, 42.8680301274912, 43.3578571286387, 43.8490335162540, 44.3414666385172, 44.8350628385566, 45.3297275233803, 45.8253652343791, 46.3218797192938, 46.8191740055340, 47.3171504747325, 47.8157109384175, 48.3147567146766, 48.8141887056904, 49.3139074760053, 49.8138133314150, 50.3138063983199, 50.8137867034288, 51.3136542536690, 51.8133091161694, 52.3126514981792, 52.8115818267888, 53.3100008283151, 53.8078096072184, 54.3049097244174, 54.8012032748703, 55.2965929642930, 55.7909821848871, 56.2842750899540, 56.7763766672728, 57.2671928111254, 57.7566303928546, 58.2445973298443, 58.7310026528181, 59.2157565713534, 59.6987705375169, 60.1799573075290, 60.6592310013724, 61.1365071602642, 61.6117028019181, 62.0847364735261, 62.5555283023992, 63.0240000442087, 63.4900751287784, 63.9536787033824, 64.4147376735109, 64.8731807410717, 65.3289384400004, 65.7819431692609, 66.2321292232214, 66.6794328193975, 67.1237921235621, 67.5651472722240, 68.0034403924850, 68.4386156192918, 68.8706191101006, 69.2993990569809, 69.7249056961888, 70.1470913152441, 70.5659102575511, 70.9813189246068, 71.3932757758436, 71.8017413261593, 72.2066781411888, 72.6080508303755, 73.0058260379057, 73.3999724315685, 73.7904606896088, 74.1772634856441, 74.5603554717132, 74.9397132595338, 75.3153154000403, 75.6871423612796, 76.0551765047418, 76.4194020602032, 76.7798050991594, 77.1363735069297, 77.4890969535081, 77.8379668632443, 78.1829763834284, 78.5241203518627, 78.8613952634932, 79.1947992361820, 79.5243319756938, 79.8499947399716, 80.1717903027764, 80.4897229167615, 80.8037982760533, 81.1140234784069, 81.4204069870039, 81.7229585919581, 82.0216893715927, 82.3166116535506, 82.6077389757973, 82.8950860475745, 83.1786687103591, 83.4585038988807, 83.7346096022504, 84.0070048252472, 84.2757095498103, 84.5407446967817, 84.8021320879401, 85.0598944083668, 85.3140551691816, 85.5646386706832, 85.8116699659280, 86.0551748247783, 86.2951796984492, 86.5317116845807, 86.7647984928596, 86.9944684112155, 87.2207502726098, 87.4436734224386, 87.6632676865654, 87.8795633399994, 88.0925910762336, 88.3023819772534, 88.5089674842271, 88.7123793688868, 88.9126497056067, 89.1098108441845, 89.3038953833309, 89.4949361448701, 89.6829661486526, 89.8680185881816, 90.0501268069521, 90.2293242755015, 90.4056445691688, 90.5791213465588, 90.7497883287071, 90.9176792789402, 91.0828279834253, 91.2452682324022, 91.4050338020896, 91.5621584372592, 91.7166758344664, 91.8686196259308, 92.0180233640546, 92.1649205065702, 92.3093444023051, 92.4513282775545, 92.5909052230488, 92.7281081815050, 92.8629699357510, 92.9955230974084, 93.1258000961244, 93.2538331693382, 93.3796543525700, 93.5032954702203, 93.6247881268665, 93.7441636990437, 93.8614533274979, 93.9766879098979, 94.0898980939930, 94.2011142712052, 94.3103665706420, 94.4176848535171, 94.5230987079678, 94.6266374442559, 94.7283300903397, 94.8282053878057, 94.9262917881474, 95.0226174493806, 95.1172102329820, 95.2100977011406, 95.3013071143112, 95.3908654290582, 95.4787992961784, 95.5651350590940, 95.6498987525033, 95.7331161012805, 95.8148125196139, 95.8950131103724, 95.9737426646922, 96.0510256617723, 96.1268862688721, 96.2013483414998, 96.2744354237853, 96.3461707490273, 96.4165772404076, 96.4856775118647, 96.5534938691173, 96.6200483108329, 96.6853625299320, 96.7494579150218, 96.8123555519521, 96.8740762254876, 96.9346404210890, 96.9940683267977, 97.0523798352169, 97.1095945455854, 97.1657317659355, 97.2208105153323, 97.2748495261873, 97.3278672466426, 97.3798818430194, 97.4309112023277, 97.4809729348311, 97.5300843766635, 97.5782625924929, 97.6255243782289, 97.6718862637686, 97.7173645157795, 97.7619751405131, 97.8057338866485, 97.8486562481603, 97.8907574672094, 97.9320525370528, 97.9725562049698, 98.0122829752020, 98.0512471119038, 98.0894626421020, 98.1269433586608, 98.1637028232512, 98.1997543693219, 98.2351111050693, 98.2697859164057, 98.3037914699225, 98.3371402158486, 98.3698443909993, 98.4019160217174, 98.4333669268027, 98.4642087204294, 98.4944528150500, 98.5241104242837, 98.5531925657901, 98.5817100641240, 98.6096735535730, 98.6370934809761, 98.6639801085206, 98.6903435165201, 98.7161936061688, 98.7415401022740, 98.7663925559657, 98.7907603473812, 98.8146526883261, 98.8380786249097, 98.8610470401551, 98.8835666565831, 98.9056460387694, 98.9272935958755, 98.9485175841521, 98.9693261094149, 98.9897271294928, 99.0097284566484, 99.0293377599695, 99.0485625677333, 99.0674102697411, 99.0858881196253, 99.1040032371268, 99.1217626103445, 99.1391730979551, 99.1562414314049, 99.1729742170724, 99.1893779384018, 99.2054589580084, 99.2212235197548, 99.2366777507984, 99.2518276636112, 99.2666791579700, 99.2812380229192, 99.2955099387048, 99.3095004786814, 99.3232151111900, 99.3366592014091, 99.3498380131779, 99.3627567107925, 99.3754203607747, 99.3878339336141, 99.4000023054832, 99.4119302599269, 99.4236224895245, 99.4350835975271, 99.4463180994682, 99.4573304247495, 99.4681249182009, 99.4787058416163, 99.4890773752641, 99.4992436193731, 99.5092085955951, 99.5189762484427, 99.5285504467039, 99.5379349848336, 99.5471335843213, 99.5561498950368, 99.5649874965529, 99.5736498994462, 99.5821405465756, 99.5904628143396, 99.5986200139115, 99.6066153924546, 99.6144521343156, 99.6221333621980, 99.6296621383148, 99.6370414655222, 99.6442742884322, 99.6513634945072, 99.6583119151344, 99.6651223266823, 99.6717974515374, 99.6783399591241, 99.6847524669052, 99.6910375413657, 99.6971976989782, 99.7032354071519, 99.7091530851642, 99.7149531050753, 99.7206377926274, 99.7262094281262, 99.7316702473083, 99.7370224421909, 99.7422681619079, 99.7474095135296, 99.7524485628683, 99.7573873352681, 99.7622278163817, 99.7669719529318, 99.7716216534590, 99.7761787890560, 99.7806451940880, 99.7850226669001, 99.7893129705113, 99.7935178332962, 99.7976389496532, 99.8016779806612, 99.8056365547233, 99.8095162681991, 99.8133186860247, 99.8170453423216, 99.8206977409938, 99.8242773563139, 99.8277856334982, 99.8312239892706, 99.8345938124168, 99.8378964643271, 99.8411332795293, 99.8443055662117, 99.8474146067362, 99.8504616581410, 99.8534479526350, 99.8563746980818, 99.8592430784747, 99.8620542544030, 99.8648093635092, 99.8675095209374, 99.8701558197732, 99.8727493314755, 99.8752911062995, 99.8777821737119, 99.8802235427982, 99.8826162026623, 99.8849611228179, 99.8872592535729, 99.8895115264063, 99.8917188543376, 99.8938821322895, 99.8960022374434, 99.8980800295876, 99.9001163514598, 99.9021120290819, 99.9040678720893, 99.9059846740529, 99.9078632127955, 99.9097042507021, 99.9115085350236, 99.9132767981752, 99.9150097580290, 99.9167081182002, 99.9183725683287, 99.9200037843546, 99.9216024287886, 99.9231691509770, 99.9247045873616, 99.9262093617345, 99.9276840854882, 99.9291293578601, 99.9305457661733, 99.9319338860717, 99.9332942817511, 99.9346275061855, 99.9359341013492, 99.9372145984344, 99.9384695180644, 99.9396993705030, 99.9409046558598, 99.9420858642906, 99.9432434761954, 99.9443779624109, 99.9454897844005, 99.9465793944397, 99.9476472357987, 99.9486937429204, 99.9497193415956, 99.9507244491347, 99.9517094745360, 99.9526748186504, 99.9536208743428, 99.9545480266513, 99.9554566529419, 99.9563471230611, 99.9572197994851, 99.9580750374663, 99.9589131851765, 99.9597345838477, 99.9605395679100, 99.9613284651267, 99.9621015967266, 99.9628592775343, 99.9636018160970, 99.9643295148095, 99.9650426700366, 99.9657415722329, 99.9664265060602, 99.9670977505031, 99.9677555789815, 99.9684002594613, 99.9690320545634, 99.9696512216694, 99.9702580130263, 99.9708526758486, 99.9714354524184, 99.9720065801833, 99.9725662918533, 99.9731148154946, 99.9736523746221, 99.9741791882902, 99.9746954711815, 99.9752014336941, 99.9756972820264, 99.9761832182614, 99.9766594404484, 99.9771261426831, 99.9775835151868, 99.9780317443833, 99.9784710129747, 99.9789015000158, 99.9793233809861, 99.9797368278619, 99.9801420091854, 99.9805390901338, 99.9809282325857, 99.9813095951875, 99.9816833334175, 99.9820495996491, 99.9824085432128, 99.9827603104566, 99.9831050448061, 99.9834428868221, 99.9837739742580, 99.9840984421161, 99.9844164227019, 99.9847280456782, 99.9850334381182, 99.9853327245562, 99.9856260270393, 99.9859134651763, 99.9861951561867, 99.9864712149482, 99.9867417540436, 99.9870068838065, 99.9872667123662, 99.9875213456915, 99.9877708876343, 99.9880154399714, 99.9882551024460, 99.9884899728086, 99.9887201468563, 99.9889457184722, 99.9891667796633, 99.9893834205983, 99.9895957296440, 99.9898037934013, 99.9900076967408, 99.9902075228367, 99.9904033532015, 99.9905952677183, 99.9907833446742, 99.9909676607913, 99.9911482912589, 99.9913253097632, 99.9914987885178, 99.9916687982934, 99.9918354084457, 99.9919986869447, 99.9921587004016, 99.9923155140964, 99.9924691920042, 99.9926197968215, 99.9927673899916, 99.9929120317296, 99.9930537810472, 99.9931926957762, 99.9933288325928, 99.9934622470401, 99.9935929935508, 99.9937211254699, 99.9938466950756, 99.9939697536015, 99.9940903512567, 99.9942085372467, 99.9943243597936, 99.9944378661551, 99.9945491026446, 99.9946581146492, 99.9947649466491, 99.9948696422350, 99.9949722441261, 99.9950727941880, 99.9951713334487, 99.9952679021166, 99.9953625395957, 99.9954552845026, 99.9955461746816, 99.9956352472207, 99.9957225384661, 99.9958080840374, 99.9958919188422, 99.9959740770901, 99.9960545923067, 99.9961334973473, 99.9962108244104, 99.9962866050506, 99.9963608701917, 99.9964336501393, 99.9965049745927, 99.9965748726578, 99.9966433728583, 99.9967105031478, 99.9967762909207, 99.9968407630238, 99.9969039457672, 99.9969658649347, 99.9970265457948, 99.9970860131107, 99.9971442911502, 99.9972014036962, 99.9972573740558, 99.9973122250703, 99.9973659791241, 99.9974186581540, 99.9974702836582, 99.9975208767052, 99.9975704579418, 99.9976190476025, 99.9976666655166, 99.9977133311174, 99.9977590634493, 99.9978038811760, 99.9978478025878, 99.9978908456097, 99.9979330278078, 99.9979743663972, 99.9980148782486, 99.9980545798955, 99.9980934875406, 99.9981316170629, 99.9981689840234, 99.9982056036724, 99.9982414909550, 99.9982766605174, 99.9983111267131, 99.9983449036084, 99.9983780049884, 99.9984104443624, 99.9984422349698, 99.9984733897851, 99.9985039215233, 99.9985338426452, 99.9985631653623, 99.9985919016422, 99.9986200632128, 99.9986476615677, 99.9986747079706, 99.9987012134599, 99.9987271888533, 99.9987526447522, 99.9987775915460, 99.9988020394162, 99.9988259983409, 99.9988494780984, 99.9988724882717, 99.9988950382520, 99.9989171372428, 99.9989387942634, 99.9989600181529, 99.9989808175735, 99.9990012010143, 99.9990211767945, 99.9990407530670, 99.9990599378216, 99.9990787388885, 99.9990971639410, 99.9991152204991, 99.9991329159326, 99.9991502574636, 99.9991672521699, 99.9991839069878, 99.9992002287148, 99.9992162240126, 99.9992318994095, 99.9992472613033, 99.9992623159639, 99.9992770695358, 99.9992915280406, 99.9993056973794, 99.9993195833354, 99.9993331915761, 99.9993465276556, 99.9993595970171, 99.9993724049947, 99.9993849568161, 99.9993972576041, 99.9994093123793, 99.9994211260620, 99.9994327034737, 99.9994440493399, 99.9994551682913, 99.9994660648661, 99.9994767435117, 99.9994872085867, 99.9994974643624, 99.9995075150247, 99.9995173646757, 99.9995270173356, 99.9995364769441, 99.9995457473622, 99.9995548323737, 99.9995637356866, 99.9995724609348, 99.9995810116796, 99.9995893914109, 99.9995976035489, 99.9996056514456, 99.9996135383856, 99.9996212675880, 99.9996288422075, 99.9996362653358, 99.9996435400027, 99.9996506691772, 99.9996576557693, 99.9996645026304, 99.9996712125553, 99.9996777882826, 99.9996842324962, 99.9996905478263, 99.9996967368506, 99.9997028020952, 99.9997087460356, 99.9997145710980, 99.9997202796597, 99.9997258740509, 99.9997313565548, 99.9997367294093, 99.9997419948072, 99.9997471548978, 99.9997522117870, 99.9997571675390, 99.9997620241764, 99.9997667836816, 99.9997714479971, 99.9997760190267, 99.9997804986361, 99.9997848886537, 99.9997891908714, 99.9997934070451, 99.9997975388957, 99.9998015881095, 99.9998055563395, 99.9998094452051, 99.9998132562938, 99.9998169911609, 99.9998206513310, 99.9998242382979, 99.9998277535258, 99.9998311984493, 99.9998345744747, 99.9998378829797, 99.9998411253148, 99.9998443028035, 99.9998474167426, 99.9998504684031, 99.9998534590305, 99.9998563898456, 99.9998592620446, 99.9998620767997, 99.9998648352599, 99.9998675385511, 99.9998701877766, 99.9998727840177, 99.9998753283341, 99.9998778217643, 99.9998802653260, 99.9998826600166, 99.9998850068135, 99.9998873066746, 99.9998895605386, 99.9998917693254, 99.9998939339365, 99.9998960552555, 99.9998981341483, 99.9999001714632, 99.9999021680320, 99.9999041246694, 99.9999060421742, 99.9999079213289, 99.9999097629007, 99.9999115676410, 99.9999133362867, 99.9999150695594, 99.9999167681668, 99.9999184328021, 99.9999200641447, 99.9999216628605, 99.9999232296021, 99.9999247650089, 99.9999262697075, 99.9999277443123, 99.9999291894250, 99.9999306056355, 99.9999319935218, 99.9999333536505, 99.9999346865766, 99.9999359928442, 99.9999372729865, 99.9999385275260, 99.9999397569747, 99.9999409618345, 99.9999421425971, 99.9999432997445, 99.9999444337490, 99.9999455450734, 99.9999466341713, 99.9999477014873, 99.9999487474570, 99.9999497725074, 99.9999507770567, 99.9999517615151, 99.9999527262843, 99.9999536717582, 99.9999545983226, 99.9999555063557, 99.9999563962282, 99.9999572683033, 99.9999581229368, 99.9999589604778, 99.9999597812679, 99.9999605856422, 99.9999613739290, 99.9999621464501, 99.9999629035209, 99.9999636454502, 99.9999643725409, 99.9999650850898, 99.9999657833878, 99.9999664677198, 99.9999671383652, 99.9999677955976, 99.9999684396855, 99.9999690708916, 99.9999696894735, 99.9999702956839, 99.9999708897700, 99.9999714719745, 99.9999720425348, 99.9999726016840, 99.9999731496501, 99.9999736866570, 99.9999742129237, 99.9999747286651, 99.9999752340917, 99.9999757294097, 99.9999762148214, 99.9999766905249, 99.9999771567143, 99.9999776135799, 99.9999780613082, 99.9999785000819, 99.9999789300802, 99.9999793514785, 99.9999797644488, 99.9999801691598, 99.9999805657765, 99.9999809544609, 99.9999813353716, 99.9999817086641, 99.9999820744907, 99.9999824330009, 99.9999827843408, 99.9999831286539, 99.9999834660808, 99.9999837967591, 99.9999841208239, 99.9999844384074, 99.9999847496392, 99.9999850546463, 99.9999853535534, 99.9999856464822, 99.9999859335526, 99.9999862148815, 99.9999864905838, 99.9999867607721, 99.9999870255566, 99.9999872850454, 99.9999875393445, 99.9999877885575, 99.9999880327864, 99.9999882721306, 99.9999885066880, 99.9999887365542, 99.9999889618231, 99.9999891825866, 99.9999893989348, 99.9999896109561, 99.9999898187370, 99.9999900223622, 99.9999902219149, 99.9999904174766, 99.9999906091271, 99.9999907969445, 99.9999909810056, 99.9999911613855, 99.9999913381577, 99.9999915113946, 99.9999916811666, 99.9999918475433, 99.9999920105924, 99.9999921703806, 99.9999923269729, 99.9999924804335, 99.9999926308248, 99.9999927782083, 99.9999929226441, 99.9999930641912, 99.9999932029074, 99.9999933388492, 99.9999934720722, 99.9999936026308, 99.9999937305782, 99.9999938559666, 99.9999939788472, 99.9999940992703, 99.9999942172849, 99.9999943329392, 99.9999944462804, 99.9999945573548, 99.9999946662077, 99.9999947728835, 99.9999948774258, 99.9999949798773, 99.9999950802798, 99.9999951786742, 99.9999952751007, 99.9999953695987, 99.9999954622067, 99.9999955529625, 99.9999956419033, 99.9999957290652, 99.9999958144839, 99.9999958981942, 99.9999959802304, 99.9999960606257, 99.9999961394132, 99.9999962166250, 99.9999962922925, 99.9999963664466, 99.9999964391177, 99.9999965103353, 99.9999965801286, 99.9999966485260, 99.9999967155555, 99.9999967812444, 99.9999968456195, 99.9999969087071, 99.9999969705330, 99.9999970311223, 99.9999970904999, 99.9999971486899, 99.9999972057161, 99.9999972616018, 99.9999973163697, 99.9999973700423, 99.9999974226415, 99.9999974741887, 99.9999975247049, 99.9999975742108, 99.9999976227266, 99.9999976702720, 99.9999977168666, 99.9999977625293, 99.9999978072787, 99.9999978511331, 99.9999978941105, 99.9999979362282, 99.9999979775037, 99.9999980179536, 99.9999980575945, 99.9999980964426, 99.9999981345138, 99.9999981718235, 99.9999982083870, 99.9999982442193, 99.9999982793349, 99.9999983137482, 99.9999983474732, 99.9999983805238, 99.9999984129133]
#Exercise 5
def euler2(diff_eq, initial, h, num_times):
fcn(N)=N+h*diff_eq(N)
ex5out=iterate(fcn, num_times, initial)
tfinal=srange(0,100+h,h)
Ex5=zip(tfinal, ex5out)
return Ex5

N_prime(N)=0.2*N*(1-N/100)
h=0.1
out5=euler2(N_prime, 10, h, 1000) ##### Good. -HK

out5

[(0.000000000000000, 10), (0.100000000000000, 10.1800000000000), (0.200000000000000, 10.3628735200000), (0.300000000000000, 10.5486531608817), (0.400000000000000, 10.7373714073976), (0.500000000000000, 10.9290606065975), (0.600000000000000, 11.1237529455809), (0.700000000000000, 11.3214804285737), (0.800000000000000, 11.5222748533262), (0.900000000000000, 11.7261677868336), (1.00000000000000, 11.9331905403773), (1.10000000000000, 12.1433741438903), (1.20000000000000, 12.3567493196484), (1.30000000000000, 12.5733464552916), (1.40000000000000, 12.7931955761805), (1.50000000000000, 13.0163263170940), (1.60000000000000, 13.2427678932773), (1.70000000000000, 13.4725490708478), (1.80000000000000, 13.7056981365714), (1.90000000000000, 13.9422428670207), (2.00000000000000, 14.1822104971285), (2.10000000000000, 14.4256276881541), (2.20000000000000, 14.6725204950778), (2.30000000000000, 14.9229143334436), (2.40000000000000, 15.1768339456718), (2.50000000000000, 15.4343033668624), (2.60000000000000, 15.6953458901155), (2.70000000000000, 15.9599840313958), (2.80000000000000, 16.2282394939672), (2.90000000000000, 16.5001331324319), (3.00000000000000, 16.7756849164029), (3.10000000000000, 17.0549138938481), (3.20000000000000, 17.3378381541397), (3.30000000000000, 17.6244747908507), (3.40000000000000, 17.9148398643370), (3.50000000000000, 18.2089483641508), (3.60000000000000, 18.5068141713282), (3.70000000000000, 18.8084500206003), (3.80000000000000, 19.1138674625768), (3.90000000000000, 19.4230768259530), (4.00000000000000, 19.7360871797947), (4.10000000000000, 20.0529062959569), (4.20000000000000, 20.3735406116931), (4.30000000000000, 20.6979951925157), (4.40000000000000, 21.0262736953681), (4.50000000000000, 21.3583783321730), (4.60000000000000, 21.6943098338204), (4.70000000000000, 22.0340674146637), (4.80000000000000, 22.3776487375901), (4.90000000000000, 22.7250498797374), (5.00000000000000, 23.0762652989248), (5.10000000000000, 23.4312878008740), (5.20000000000000, 23.7901085072900), (5.30000000000000, 24.1527168248781), (5.40000000000000, 24.5191004153711), (5.50000000000000, 24.8892451666427), (5.60000000000000, 25.2631351649825), (5.70000000000000, 25.6407526686093), (5.80000000000000, 26.0220780824990), (5.90000000000000, 26.4070899346026), (5.99999999999999, 26.7957648535318), (6.09999999999999, 27.1880775477853), (6.19999999999999, 27.5840007865921), (6.29999999999999, 27.9835053824450), (6.39999999999999, 28.3865601753961), (6.49999999999999, 28.7931320191857), (6.59999999999999, 29.2031857692746), (6.69999999999999, 29.6166842728451), (6.79999999999999, 30.0335883608386), (6.89999999999999, 30.4538568420897), (6.99999999999999, 30.8774464996198), (7.09999999999999, 31.3043120891448), (7.19999999999999, 31.7344063398528), (7.29999999999999, 32.1676799575012), (7.39999999999999, 32.6040816298816), (7.49999999999999, 33.0435580346936), (7.59999999999999, 33.4860538498691), (7.69999999999999, 33.9315117663792), (7.79999999999999, 34.3798725035564), (7.89999999999999, 34.8310748269554), (7.99999999999999, 35.2850555687743), (8.09999999999999, 35.7417496508515), (8.19999999999999, 36.2010901102477), (8.29999999999999, 36.6630081274186), (8.39999999999999, 37.1274330569767), (8.49999999999999, 37.5942924610362), (8.59999999999999, 38.0635121451277), (8.69999999999999, 38.5350161966658), (8.79999999999998, 39.0087270259437), (8.89999999999998, 39.4845654096256), (8.99999999999998, 39.9624505367008), (9.09999999999998, 40.4423000568551), (9.19999999999998, 40.9240301312145), (9.29999999999998, 41.4075554854027), (9.39999999999998, 41.8927894648554), (9.49999999999998, 42.3796440923231), (9.59999999999998, 42.8680301274912), (9.69999999999998, 43.3578571286387), (9.79999999999998, 43.8490335162540), (9.89999999999998, 44.3414666385172), (9.99999999999998, 44.8350628385566), (10.1000000000000, 45.3297275233803), (10.2000000000000, 45.8253652343791), (10.3000000000000, 46.3218797192938), (10.4000000000000, 46.8191740055340), (10.5000000000000, 47.3171504747325), (10.6000000000000, 47.8157109384175), (10.7000000000000, 48.3147567146766), (10.8000000000000, 48.8141887056904), (10.9000000000000, 49.3139074760053), (11.0000000000000, 49.8138133314150), (11.1000000000000, 50.3138063983199), (11.2000000000000, 50.8137867034288), (11.3000000000000, 51.3136542536690), (11.4000000000000, 51.8133091161694), (11.5000000000000, 52.3126514981792), (11.6000000000000, 52.8115818267888), (11.7000000000000, 53.3100008283151), (11.8000000000000, 53.8078096072184), (11.9000000000000, 54.3049097244174), (12.0000000000000, 54.8012032748703), (12.1000000000000, 55.2965929642930), (12.2000000000000, 55.7909821848871), (12.3000000000000, 56.2842750899540), (12.4000000000000, 56.7763766672728), (12.5000000000000, 57.2671928111254), (12.6000000000000, 57.7566303928546), (12.7000000000000, 58.2445973298443), (12.8000000000000, 58.7310026528181), (12.9000000000000, 59.2157565713534), (13.0000000000000, 59.6987705375169), (13.1000000000000, 60.1799573075290), (13.2000000000000, 60.6592310013724), (13.3000000000000, 61.1365071602642), (13.4000000000000, 61.6117028019181), (13.5000000000000, 62.0847364735261), (13.6000000000000, 62.5555283023992), (13.7000000000000, 63.0240000442087), (13.8000000000000, 63.4900751287784), (13.9000000000000, 63.9536787033824), (14.0000000000000, 64.4147376735109), (14.1000000000000, 64.8731807410717), (14.2000000000000, 65.3289384400004), (14.3000000000000, 65.7819431692609), (14.4000000000000, 66.2321292232214), (14.5000000000000, 66.6794328193975), (14.6000000000000, 67.1237921235621), (14.7000000000000, 67.5651472722240), (14.8000000000000, 68.0034403924850), (14.9000000000000, 68.4386156192918), (15.0000000000000, 68.8706191101006), (15.1000000000000, 69.2993990569809), (15.2000000000000, 69.7249056961888), (15.3000000000000, 70.1470913152441), (15.4000000000000, 70.5659102575511), (15.5000000000000, 70.9813189246068), (15.6000000000000, 71.3932757758436), (15.7000000000000, 71.8017413261593), (15.8000000000000, 72.2066781411888), (15.9000000000000, 72.6080508303755), (16.0000000000000, 73.0058260379057), (16.1000000000000, 73.3999724315685), (16.2000000000000, 73.7904606896088), (16.3000000000000, 74.1772634856441), (16.4000000000000, 74.5603554717132), (16.5000000000000, 74.9397132595338), (16.6000000000000, 75.3153154000403), (16.7000000000000, 75.6871423612796), (16.8000000000000, 76.0551765047418), (16.9000000000000, 76.4194020602032), (17.0000000000000, 76.7798050991594), (17.1000000000000, 77.1363735069297), (17.2000000000000, 77.4890969535081), (17.3000000000000, 77.8379668632443), (17.4000000000000, 78.1829763834284), (17.5000000000000, 78.5241203518627), (17.6000000000000, 78.8613952634932), (17.7000000000000, 79.1947992361820), (17.8000000000000, 79.5243319756938), (17.9000000000000, 79.8499947399716), (18.0000000000000, 80.1717903027764), (18.1000000000000, 80.4897229167615), (18.2000000000000, 80.8037982760533), (18.3000000000000, 81.1140234784069), (18.4000000000000, 81.4204069870039), (18.5000000000000, 81.7229585919581), (18.6000000000000, 82.0216893715927), (18.7000000000000, 82.3166116535506), (18.8000000000000, 82.6077389757973), (18.9000000000000, 82.8950860475745), (19.0000000000000, 83.1786687103591), (19.1000000000000, 83.4585038988807), (19.2000000000000, 83.7346096022504), (19.3000000000000, 84.0070048252472), (19.4000000000000, 84.2757095498103), (19.5000000000000, 84.5407446967817), (19.6000000000000, 84.8021320879401), (19.7000000000000, 85.0598944083668), (19.8000000000000, 85.3140551691816), (19.9000000000000, 85.5646386706832), (20.0000000000000, 85.8116699659280), (20.1000000000000, 86.0551748247783), (20.2000000000000, 86.2951796984492), (20.3000000000000, 86.5317116845807), (20.4000000000000, 86.7647984928596), (20.5000000000000, 86.9944684112155), (20.6000000000000, 87.2207502726098), (20.7000000000000, 87.4436734224386), (20.8000000000000, 87.6632676865654), (20.9000000000000, 87.8795633399994), (21.0000000000000, 88.0925910762336), (21.1000000000000, 88.3023819772534), (21.2000000000000, 88.5089674842271), (21.3000000000000, 88.7123793688868), (21.4000000000000, 88.9126497056067), (21.5000000000000, 89.1098108441845), (21.6000000000000, 89.3038953833309), (21.7000000000000, 89.4949361448701), (21.8000000000000, 89.6829661486526), (21.9000000000000, 89.8680185881816), (22.0000000000000, 90.0501268069521), (22.1000000000000, 90.2293242755015), (22.2000000000000, 90.4056445691688), (22.3000000000000, 90.5791213465588), (22.4000000000000, 90.7497883287071), (22.5000000000000, 90.9176792789402), (22.6000000000001, 91.0828279834253), (22.7000000000001, 91.2452682324022), (22.8000000000001, 91.4050338020896), (22.9000000000001, 91.5621584372592), (23.0000000000001, 91.7166758344664), (23.1000000000001, 91.8686196259308), (23.2000000000001, 92.0180233640546), (23.3000000000001, 92.1649205065702), (23.4000000000001, 92.3093444023051), (23.5000000000001, 92.4513282775545), (23.6000000000001, 92.5909052230488), (23.7000000000001, 92.7281081815050), (23.8000000000001, 92.8629699357510), (23.9000000000001, 92.9955230974084), (24.0000000000001, 93.1258000961244), (24.1000000000001, 93.2538331693382), (24.2000000000001, 93.3796543525700), (24.3000000000001, 93.5032954702203), (24.4000000000001, 93.6247881268665), (24.5000000000001, 93.7441636990437), (24.6000000000001, 93.8614533274979), (24.7000000000001, 93.9766879098979), (24.8000000000001, 94.0898980939930), (24.9000000000001, 94.2011142712052), (25.0000000000001, 94.3103665706420), (25.1000000000001, 94.4176848535171), (25.2000000000001, 94.5230987079678), (25.3000000000001, 94.6266374442559), (25.4000000000001, 94.7283300903397), (25.5000000000001, 94.8282053878057), (25.6000000000001, 94.9262917881474), (25.7000000000001, 95.0226174493806), (25.8000000000001, 95.1172102329820), (25.9000000000001, 95.2100977011406), (26.0000000000001, 95.3013071143112), (26.1000000000001, 95.3908654290582), (26.2000000000001, 95.4787992961784), (26.3000000000001, 95.5651350590940), (26.4000000000001, 95.6498987525033), (26.5000000000001, 95.7331161012805), (26.6000000000001, 95.8148125196139), (26.7000000000001, 95.8950131103724), (26.8000000000001, 95.9737426646922), (26.9000000000001, 96.0510256617723), (27.0000000000001, 96.1268862688721), (27.1000000000001, 96.2013483414998), (27.2000000000001, 96.2744354237853), (27.3000000000001, 96.3461707490273), (27.4000000000001, 96.4165772404076), (27.5000000000001, 96.4856775118647), (27.6000000000001, 96.5534938691173), (27.7000000000001, 96.6200483108329), (27.8000000000001, 96.6853625299320), (27.9000000000001, 96.7494579150218), (28.0000000000001, 96.8123555519521), (28.1000000000001, 96.8740762254876), (28.2000000000001, 96.9346404210890), (28.3000000000001, 96.9940683267977), (28.4000000000001, 97.0523798352169), (28.5000000000001, 97.1095945455854), (28.6000000000001, 97.1657317659355), (28.7000000000001, 97.2208105153323), (28.8000000000001, 97.2748495261873), (28.9000000000001, 97.3278672466426), (29.0000000000001, 97.3798818430194), (29.1000000000001, 97.4309112023277), (29.2000000000001, 97.4809729348311), (29.3000000000001, 97.5300843766635), (29.4000000000001, 97.5782625924929), (29.5000000000001, 97.6255243782289), (29.6000000000002, 97.6718862637686), (29.7000000000002, 97.7173645157795), (29.8000000000002, 97.7619751405131), (29.9000000000002, 97.8057338866485), (30.0000000000002, 97.8486562481603), (30.1000000000002, 97.8907574672094), (30.2000000000002, 97.9320525370528), (30.3000000000002, 97.9725562049698), (30.4000000000002, 98.0122829752020), (30.5000000000002, 98.0512471119038), (30.6000000000002, 98.0894626421020), (30.7000000000002, 98.1269433586608), (30.8000000000002, 98.1637028232512), (30.9000000000002, 98.1997543693219), (31.0000000000002, 98.2351111050693), (31.1000000000002, 98.2697859164057), (31.2000000000002, 98.3037914699225), (31.3000000000002, 98.3371402158486), (31.4000000000002, 98.3698443909993), (31.5000000000002, 98.4019160217174), (31.6000000000002, 98.4333669268027), (31.7000000000002, 98.4642087204294), (31.8000000000002, 98.4944528150500), (31.9000000000002, 98.5241104242837), (32.0000000000002, 98.5531925657901), (32.1000000000002, 98.5817100641240), (32.2000000000002, 98.6096735535730), (32.3000000000002, 98.6370934809761), (32.4000000000002, 98.6639801085206), (32.5000000000002, 98.6903435165201), (32.6000000000002, 98.7161936061688), (32.7000000000002, 98.7415401022740), (32.8000000000002, 98.7663925559657), (32.9000000000002, 98.7907603473812), (33.0000000000002, 98.8146526883261), (33.1000000000002, 98.8380786249097), (33.2000000000002, 98.8610470401551), (33.3000000000002, 98.8835666565831), (33.4000000000002, 98.9056460387694), (33.5000000000002, 98.9272935958755), (33.6000000000002, 98.9485175841521), (33.7000000000002, 98.9693261094149), (33.8000000000002, 98.9897271294928), (33.9000000000002, 99.0097284566484), (34.0000000000002, 99.0293377599695), (34.1000000000002, 99.0485625677333), (34.2000000000002, 99.0674102697411), (34.3000000000002, 99.0858881196253), (34.4000000000002, 99.1040032371268), (34.5000000000002, 99.1217626103445), (34.6000000000002, 99.1391730979551), (34.7000000000002, 99.1562414314049), (34.8000000000002, 99.1729742170724), (34.9000000000002, 99.1893779384018), (35.0000000000002, 99.2054589580084), (35.1000000000002, 99.2212235197548), (35.2000000000002, 99.2366777507984), (35.3000000000002, 99.2518276636112), (35.4000000000002, 99.2666791579700), (35.5000000000002, 99.2812380229192), (35.6000000000002, 99.2955099387048), (35.7000000000002, 99.3095004786814), (35.8000000000002, 99.3232151111900), (35.9000000000002, 99.3366592014091), (36.0000000000002, 99.3498380131779), (36.1000000000002, 99.3627567107925), (36.2000000000002, 99.3754203607747), (36.3000000000002, 99.3878339336141), (36.4000000000002, 99.4000023054832), (36.5000000000002, 99.4119302599269), (36.6000000000003, 99.4236224895245), (36.7000000000003, 99.4350835975271), (36.8000000000003, 99.4463180994682), (36.9000000000003, 99.4573304247495), (37.0000000000003, 99.4681249182009), (37.1000000000003, 99.4787058416163), (37.2000000000003, 99.4890773752641), (37.3000000000003, 99.4992436193731), (37.4000000000003, 99.5092085955951), (37.5000000000003, 99.5189762484427), (37.6000000000003, 99.5285504467039), (37.7000000000003, 99.5379349848336), (37.8000000000003, 99.5471335843213), (37.9000000000003, 99.5561498950368), (38.0000000000003, 99.5649874965529), (38.1000000000003, 99.5736498994462), (38.2000000000003, 99.5821405465756), (38.3000000000003, 99.5904628143396), (38.4000000000003, 99.5986200139115), (38.5000000000003, 99.6066153924546), (38.6000000000003, 99.6144521343156), (38.7000000000003, 99.6221333621980), (38.8000000000003, 99.6296621383148), (38.9000000000003, 99.6370414655222), (39.0000000000003, 99.6442742884322), (39.1000000000003, 99.6513634945072), (39.2000000000003, 99.6583119151344), (39.3000000000003, 99.6651223266823), (39.4000000000003, 99.6717974515374), (39.5000000000003, 99.6783399591241), (39.6000000000003, 99.6847524669052), (39.7000000000003, 99.6910375413657), (39.8000000000003, 99.6971976989782), (39.9000000000003, 99.7032354071519), (40.0000000000003, 99.7091530851642), (40.1000000000003, 99.7149531050753), (40.2000000000003, 99.7206377926274), (40.3000000000003, 99.7262094281262), (40.4000000000003, 99.7316702473083), (40.5000000000003, 99.7370224421909), (40.6000000000003, 99.7422681619079), (40.7000000000003, 99.7474095135296), (40.8000000000003, 99.7524485628683), (40.9000000000003, 99.7573873352681), (41.0000000000003, 99.7622278163817), (41.1000000000003, 99.7669719529318), (41.2000000000003, 99.7716216534590), (41.3000000000003, 99.7761787890560), (41.4000000000003, 99.7806451940880), (41.5000000000003, 99.7850226669001), (41.6000000000003, 99.7893129705113), (41.7000000000003, 99.7935178332962), (41.8000000000003, 99.7976389496532), (41.9000000000003, 99.8016779806612), (42.0000000000003, 99.8056365547233), (42.1000000000003, 99.8095162681991), (42.2000000000003, 99.8133186860247), (42.3000000000003, 99.8170453423216), (42.4000000000003, 99.8206977409938), (42.5000000000003, 99.8242773563139), (42.6000000000003, 99.8277856334982), (42.7000000000003, 99.8312239892706), (42.8000000000003, 99.8345938124168), (42.9000000000003, 99.8378964643271), (43.0000000000003, 99.8411332795293), (43.1000000000003, 99.8443055662117), (43.2000000000003, 99.8474146067362), (43.3000000000003, 99.8504616581410), (43.4000000000003, 99.8534479526350), (43.5000000000003, 99.8563746980818), (43.6000000000003, 99.8592430784747), (43.7000000000004, 99.8620542544030), (43.8000000000004, 99.8648093635092), (43.9000000000004, 99.8675095209374), (44.0000000000004, 99.8701558197732), (44.1000000000004, 99.8727493314755), (44.2000000000004, 99.8752911062995), (44.3000000000004, 99.8777821737119), (44.4000000000004, 99.8802235427982), (44.5000000000004, 99.8826162026623), (44.6000000000004, 99.8849611228179), (44.7000000000004, 99.8872592535729), (44.8000000000004, 99.8895115264063), (44.9000000000004, 99.8917188543376), (45.0000000000004, 99.8938821322895), (45.1000000000004, 99.8960022374434), (45.2000000000004, 99.8980800295876), (45.3000000000004, 99.9001163514598), (45.4000000000004, 99.9021120290819), (45.5000000000004, 99.9040678720893), (45.6000000000004, 99.9059846740529), (45.7000000000004, 99.9078632127955), (45.8000000000004, 99.9097042507021), (45.9000000000004, 99.9115085350236), (46.0000000000004, 99.9132767981752), (46.1000000000004, 99.9150097580290), (46.2000000000004, 99.9167081182002), (46.3000000000004, 99.9183725683287), (46.4000000000004, 99.9200037843546), (46.5000000000004, 99.9216024287886), (46.6000000000004, 99.9231691509770), (46.7000000000004, 99.9247045873616), (46.8000000000004, 99.9262093617345), (46.9000000000004, 99.9276840854882), (47.0000000000004, 99.9291293578601), (47.1000000000004, 99.9305457661733), (47.2000000000004, 99.9319338860717), (47.3000000000004, 99.9332942817511), (47.4000000000004, 99.9346275061855), (47.5000000000004, 99.9359341013492), (47.6000000000004, 99.9372145984344), (47.7000000000004, 99.9384695180644), (47.8000000000004, 99.9396993705030), (47.9000000000004, 99.9409046558598), (48.0000000000004, 99.9420858642906), (48.1000000000004, 99.9432434761954), (48.2000000000004, 99.9443779624109), (48.3000000000004, 99.9454897844005), (48.4000000000004, 99.9465793944397), (48.5000000000004, 99.9476472357987), (48.6000000000004, 99.9486937429204), (48.7000000000004, 99.9497193415956), (48.8000000000004, 99.9507244491347), (48.9000000000004, 99.9517094745360), (49.0000000000004, 99.9526748186504), (49.1000000000004, 99.9536208743428), (49.2000000000004, 99.9545480266513), (49.3000000000004, 99.9554566529419), (49.4000000000004, 99.9563471230611), (49.5000000000004, 99.9572197994851), (49.6000000000004, 99.9580750374663), (49.7000000000004, 99.9589131851765), (49.8000000000004, 99.9597345838477), (49.9000000000004, 99.9605395679100), (50.0000000000004, 99.9613284651267), (50.1000000000004, 99.9621015967266), (50.2000000000004, 99.9628592775343), (50.3000000000004, 99.9636018160970), (50.4000000000004, 99.9643295148095), (50.5000000000004, 99.9650426700366), (50.6000000000004, 99.9657415722329), (50.7000000000005, 99.9664265060602), (50.8000000000005, 99.9670977505031), (50.9000000000005, 99.9677555789815), (51.0000000000005, 99.9684002594613), (51.1000000000005, 99.9690320545634), (51.2000000000005, 99.9696512216694), (51.3000000000005, 99.9702580130263), (51.4000000000005, 99.9708526758486), (51.5000000000005, 99.9714354524184), (51.6000000000005, 99.9720065801833), (51.7000000000005, 99.9725662918533), (51.8000000000005, 99.9731148154946), (51.9000000000005, 99.9736523746221), (52.0000000000005, 99.9741791882902), (52.1000000000005, 99.9746954711815), (52.2000000000005, 99.9752014336941), (52.3000000000005, 99.9756972820264), (52.4000000000005, 99.9761832182614), (52.5000000000005, 99.9766594404484), (52.6000000000005, 99.9771261426831), (52.7000000000005, 99.9775835151868), (52.8000000000005, 99.9780317443833), (52.9000000000005, 99.9784710129747), (53.0000000000005, 99.9789015000158), (53.1000000000005, 99.9793233809861), (53.2000000000005, 99.9797368278619), (53.3000000000005, 99.9801420091854), (53.4000000000005, 99.9805390901338), (53.5000000000005, 99.9809282325857), (53.6000000000005, 99.9813095951875), (53.7000000000005, 99.9816833334175), (53.8000000000005, 99.9820495996491), (53.9000000000005, 99.9824085432128), (54.0000000000005, 99.9827603104566), (54.1000000000005, 99.9831050448061), (54.2000000000005, 99.9834428868221), (54.3000000000005, 99.9837739742580), (54.4000000000005, 99.9840984421161), (54.5000000000005, 99.9844164227019), (54.6000000000005, 99.9847280456782), (54.7000000000005, 99.9850334381182), (54.8000000000005, 99.9853327245562), (54.9000000000005, 99.9856260270393), (55.0000000000005, 99.9859134651763), (55.1000000000005, 99.9861951561867), (55.2000000000005, 99.9864712149482), (55.3000000000005, 99.9867417540436), (55.4000000000005, 99.9870068838065), (55.5000000000005, 99.9872667123662), (55.6000000000005, 99.9875213456915), (55.7000000000005, 99.9877708876343), (55.8000000000005, 99.9880154399714), (55.9000000000005, 99.9882551024460), (56.0000000000005, 99.9884899728086), (56.1000000000005, 99.9887201468563), (56.2000000000005, 99.9889457184722), (56.3000000000005, 99.9891667796633), (56.4000000000005, 99.9893834205983), (56.5000000000005, 99.9895957296440), (56.6000000000005, 99.9898037934013), (56.7000000000005, 99.9900076967408), (56.8000000000005, 99.9902075228367), (56.9000000000005, 99.9904033532015), (57.0000000000005, 99.9905952677183), (57.1000000000005, 99.9907833446742), (57.2000000000005, 99.9909676607913), (57.3000000000005, 99.9911482912589), (57.4000000000005, 99.9913253097632), (57.5000000000005, 99.9914987885178), (57.6000000000005, 99.9916687982934), (57.7000000000005, 99.9918354084457), (57.8000000000006, 99.9919986869447), (57.9000000000006, 99.9921587004016), (58.0000000000006, 99.9923155140964), (58.1000000000006, 99.9924691920042), (58.2000000000006, 99.9926197968215), (58.3000000000006, 99.9927673899916), (58.4000000000006, 99.9929120317296), (58.5000000000006, 99.9930537810472), (58.6000000000006, 99.9931926957762), (58.7000000000006, 99.9933288325928), (58.8000000000006, 99.9934622470401), (58.9000000000006, 99.9935929935508), (59.0000000000006, 99.9937211254699), (59.1000000000006, 99.9938466950756), (59.2000000000006, 99.9939697536015), (59.3000000000006, 99.9940903512567), (59.4000000000006, 99.9942085372467), (59.5000000000006, 99.9943243597936), (59.6000000000006, 99.9944378661551), (59.7000000000006, 99.9945491026446), (59.8000000000006, 99.9946581146492), (59.9000000000006, 99.9947649466491), (60.0000000000006, 99.9948696422350), (60.1000000000006, 99.9949722441261), (60.2000000000006, 99.9950727941880), (60.3000000000006, 99.9951713334487), (60.4000000000006, 99.9952679021166), (60.5000000000006, 99.9953625395957), (60.6000000000006, 99.9954552845026), (60.7000000000006, 99.9955461746816), (60.8000000000006, 99.9956352472207), (60.9000000000006, 99.9957225384661), (61.0000000000006, 99.9958080840374), (61.1000000000006, 99.9958919188422), (61.2000000000006, 99.9959740770901), (61.3000000000006, 99.9960545923067), (61.4000000000006, 99.9961334973473), (61.5000000000006, 99.9962108244104), (61.6000000000006, 99.9962866050506), (61.7000000000006, 99.9963608701917), (61.8000000000006, 99.9964336501393), (61.9000000000006, 99.9965049745927), (62.0000000000006, 99.9965748726578), (62.1000000000006, 99.9966433728583), (62.2000000000006, 99.9967105031478), (62.3000000000006, 99.9967762909207), (62.4000000000006, 99.9968407630238), (62.5000000000006, 99.9969039457672), (62.6000000000006, 99.9969658649347), (62.7000000000006, 99.9970265457948), (62.8000000000006, 99.9970860131107), (62.9000000000006, 99.9971442911502), (63.0000000000006, 99.9972014036962), (63.1000000000006, 99.9972573740558), (63.2000000000006, 99.9973122250703), (63.3000000000006, 99.9973659791241), (63.4000000000006, 99.9974186581540), (63.5000000000006, 99.9974702836582), (63.6000000000006, 99.9975208767052), (63.7000000000006, 99.9975704579418), (63.8000000000006, 99.9976190476025), (63.9000000000006, 99.9976666655166), (64.0000000000006, 99.9977133311174), (64.1000000000006, 99.9977590634493), (64.2000000000006, 99.9978038811760), (64.3000000000006, 99.9978478025878), (64.4000000000006, 99.9978908456097), (64.5000000000006, 99.9979330278078), (64.6000000000006, 99.9979743663972), (64.7000000000006, 99.9980148782486), (64.8000000000006, 99.9980545798955), (64.9000000000006, 99.9980934875406), (65.0000000000006, 99.9981316170629), (65.1000000000006, 99.9981689840234), (65.2000000000006, 99.9982056036724), (65.3000000000006, 99.9982414909550), (65.4000000000006, 99.9982766605174), (65.5000000000006, 99.9983111267131), (65.6000000000005, 99.9983449036084), (65.7000000000005, 99.9983780049884), (65.8000000000005, 99.9984104443624), (65.9000000000005, 99.9984422349698), (66.0000000000005, 99.9984733897851), (66.1000000000005, 99.9985039215233), (66.2000000000005, 99.9985338426452), (66.3000000000005, 99.9985631653623), (66.4000000000005, 99.9985919016422), (66.5000000000005, 99.9986200632128), (66.6000000000005, 99.9986476615677), (66.7000000000005, 99.9986747079706), (66.8000000000005, 99.9987012134599), (66.9000000000005, 99.9987271888533), (67.0000000000005, 99.9987526447522), (67.1000000000005, 99.9987775915460), (67.2000000000005, 99.9988020394162), (67.3000000000005, 99.9988259983409), (67.4000000000004, 99.9988494780984), (67.5000000000004, 99.9988724882717), (67.6000000000004, 99.9988950382520), (67.7000000000004, 99.9989171372428), (67.8000000000004, 99.9989387942634), (67.9000000000004, 99.9989600181529), (68.0000000000004, 99.9989808175735), (68.1000000000004, 99.9990012010143), (68.2000000000004, 99.9990211767945), (68.3000000000004, 99.9990407530670), (68.4000000000004, 99.9990599378216), (68.5000000000004, 99.9990787388885), (68.6000000000004, 99.9990971639410), (68.7000000000004, 99.9991152204991), (68.8000000000004, 99.9991329159326), (68.9000000000004, 99.9991502574636), (69.0000000000004, 99.9991672521699), (69.1000000000003, 99.9991839069878), (69.2000000000003, 99.9992002287148), (69.3000000000003, 99.9992162240126), (69.4000000000003, 99.9992318994095), (69.5000000000003, 99.9992472613033), (69.6000000000003, 99.9992623159639), (69.7000000000003, 99.9992770695358), (69.8000000000003, 99.9992915280406), (69.9000000000003, 99.9993056973794), (70.0000000000003, 99.9993195833354), (70.1000000000003, 99.9993331915761), (70.2000000000003, 99.9993465276556), (70.3000000000003, 99.9993595970171), (70.4000000000003, 99.9993724049947), (70.5000000000003, 99.9993849568161), (70.6000000000003, 99.9993972576041), (70.7000000000003, 99.9994093123793), (70.8000000000003, 99.9994211260620), (70.9000000000002, 99.9994327034737), (71.0000000000002, 99.9994440493399), (71.1000000000002, 99.9994551682913), (71.2000000000002, 99.9994660648661), (71.3000000000002, 99.9994767435117), (71.4000000000002, 99.9994872085867), (71.5000000000002, 99.9994974643624), (71.6000000000002, 99.9995075150247), (71.7000000000002, 99.9995173646757), (71.8000000000002, 99.9995270173356), (71.9000000000002, 99.9995364769441), (72.0000000000002, 99.9995457473622), (72.1000000000002, 99.9995548323737), (72.2000000000002, 99.9995637356866), (72.3000000000002, 99.9995724609348), (72.4000000000002, 99.9995810116796), (72.5000000000002, 99.9995893914109), (72.6000000000002, 99.9995976035489), (72.7000000000001, 99.9996056514456), (72.8000000000001, 99.9996135383856), (72.9000000000001, 99.9996212675880), (73.0000000000001, 99.9996288422075), (73.1000000000001, 99.9996362653358), (73.2000000000001, 99.9996435400027), (73.3000000000001, 99.9996506691772), (73.4000000000001, 99.9996576557693), (73.5000000000001, 99.9996645026304), (73.6000000000001, 99.9996712125553), (73.7000000000001, 99.9996777882826), (73.8000000000001, 99.9996842324962), (73.9000000000001, 99.9996905478263), (74.0000000000001, 99.9996967368506), (74.1000000000001, 99.9997028020952), (74.2000000000001, 99.9997087460356), (74.3000000000001, 99.9997145710980), (74.4000000000000, 99.9997202796597), (74.5000000000000, 99.9997258740509), (74.6000000000000, 99.9997313565548), (74.7000000000000, 99.9997367294093), (74.8000000000000, 99.9997419948072), (74.9000000000000, 99.9997471548978), (75.0000000000000, 99.9997522117870), (75.1000000000000, 99.9997571675390), (75.2000000000000, 99.9997620241764), (75.3000000000000, 99.9997667836816), (75.4000000000000, 99.9997714479971), (75.5000000000000, 99.9997760190267), (75.6000000000000, 99.9997804986361), (75.7000000000000, 99.9997848886537), (75.8000000000000, 99.9997891908714), (75.9000000000000, 99.9997934070451), (76.0000000000000, 99.9997975388957), (76.1000000000000, 99.9998015881095), (76.1999999999999, 99.9998055563395), (76.2999999999999, 99.9998094452051), (76.3999999999999, 99.9998132562938), (76.4999999999999, 99.9998169911609), (76.5999999999999, 99.9998206513310), (76.6999999999999, 99.9998242382979), (76.7999999999999, 99.9998277535258), (76.8999999999999, 99.9998311984493), (76.9999999999999, 99.9998345744747), (77.0999999999999, 99.9998378829797), (77.1999999999999, 99.9998411253148), (77.2999999999999, 99.9998443028035), (77.3999999999999, 99.9998474167426), (77.4999999999999, 99.9998504684031), (77.5999999999999, 99.9998534590305), (77.6999999999999, 99.9998563898456), (77.7999999999999, 99.9998592620446), (77.8999999999998, 99.9998620767997), (77.9999999999998, 99.9998648352599), (78.0999999999998, 99.9998675385511), (78.1999999999998, 99.9998701877766), (78.2999999999998, 99.9998727840177), (78.3999999999998, 99.9998753283341), (78.4999999999998, 99.9998778217643), (78.5999999999998, 99.9998802653260), (78.6999999999998, 99.9998826600166), (78.7999999999998, 99.9998850068135), (78.8999999999998, 99.9998873066746), (78.9999999999998, 99.9998895605386), (79.0999999999998, 99.9998917693254), (79.1999999999998, 99.9998939339365), (79.2999999999998, 99.9998960552555), (79.3999999999998, 99.9998981341483), (79.4999999999998, 99.9999001714632), (79.5999999999998, 99.9999021680320), (79.6999999999997, 99.9999041246694), (79.7999999999997, 99.9999060421742), (79.8999999999997, 99.9999079213289), (79.9999999999997, 99.9999097629007), (80.0999999999997, 99.9999115676410), (80.1999999999997, 99.9999133362867), (80.2999999999997, 99.9999150695594), (80.3999999999997, 99.9999167681668), (80.4999999999997, 99.9999184328021), (80.5999999999997, 99.9999200641447), (80.6999999999997, 99.9999216628605), (80.7999999999997, 99.9999232296021), (80.8999999999997, 99.9999247650089), (80.9999999999997, 99.9999262697075), (81.0999999999997, 99.9999277443123), (81.1999999999997, 99.9999291894250), (81.2999999999997, 99.9999306056355), (81.3999999999997, 99.9999319935218), (81.4999999999996, 99.9999333536505), (81.5999999999996, 99.9999346865766), (81.6999999999996, 99.9999359928442), (81.7999999999996, 99.9999372729865), (81.8999999999996, 99.9999385275260), (81.9999999999996, 99.9999397569747), (82.0999999999996, 99.9999409618345), (82.1999999999996, 99.9999421425971), (82.2999999999996, 99.9999432997445), (82.3999999999996, 99.9999444337490), (82.4999999999996, 99.9999455450734), (82.5999999999996, 99.9999466341713), (82.6999999999996, 99.9999477014873), (82.7999999999996, 99.9999487474570), (82.8999999999996, 99.9999497725074), (82.9999999999996, 99.9999507770567), (83.0999999999996, 99.9999517615151), (83.1999999999995, 99.9999527262843), (83.2999999999995, 99.9999536717582), (83.3999999999995, 99.9999545983226), (83.4999999999995, 99.9999555063557), (83.5999999999995, 99.9999563962282), (83.6999999999995, 99.9999572683033), (83.7999999999995, 99.9999581229368), (83.8999999999995, 99.9999589604778), (83.9999999999995, 99.9999597812679), (84.0999999999995, 99.9999605856422), (84.1999999999995, 99.9999613739290), (84.2999999999995, 99.9999621464501), (84.3999999999995, 99.9999629035209), (84.4999999999995, 99.9999636454502), (84.5999999999995, 99.9999643725409), (84.6999999999995, 99.9999650850898), (84.7999999999995, 99.9999657833878), (84.8999999999995, 99.9999664677198), (84.9999999999994, 99.9999671383652), (85.0999999999994, 99.9999677955976), (85.1999999999994, 99.9999684396855), (85.2999999999994, 99.9999690708916), (85.3999999999994, 99.9999696894735), (85.4999999999994, 99.9999702956839), (85.5999999999994, 99.9999708897700), (85.6999999999994, 99.9999714719745), (85.7999999999994, 99.9999720425348), (85.8999999999994, 99.9999726016840), (85.9999999999994, 99.9999731496501), (86.0999999999994, 99.9999736866570), (86.1999999999994, 99.9999742129237), (86.2999999999994, 99.9999747286651), (86.3999999999994, 99.9999752340917), (86.4999999999994, 99.9999757294097), (86.5999999999994, 99.9999762148214), (86.6999999999993, 99.9999766905249), (86.7999999999993, 99.9999771567143), (86.8999999999993, 99.9999776135799), (86.9999999999993, 99.9999780613082), (87.0999999999993, 99.9999785000819), (87.1999999999993, 99.9999789300802), (87.2999999999993, 99.9999793514785), (87.3999999999993, 99.9999797644488), (87.4999999999993, 99.9999801691598), (87.5999999999993, 99.9999805657765), (87.6999999999993, 99.9999809544609), (87.7999999999993, 99.9999813353716), (87.8999999999993, 99.9999817086641), (87.9999999999993, 99.9999820744907), (88.0999999999993, 99.9999824330009), (88.1999999999993, 99.9999827843408), (88.2999999999993, 99.9999831286539), (88.3999999999993, 99.9999834660808), (88.4999999999992, 99.9999837967591), (88.5999999999992, 99.9999841208239), (88.6999999999992, 99.9999844384074), (88.7999999999992, 99.9999847496392), (88.8999999999992, 99.9999850546463), (88.9999999999992, 99.9999853535534), (89.0999999999992, 99.9999856464822), (89.1999999999992, 99.9999859335526), (89.2999999999992, 99.9999862148815), (89.3999999999992, 99.9999864905838), (89.4999999999992, 99.9999867607721), (89.5999999999992, 99.9999870255566), (89.6999999999992, 99.9999872850454), (89.7999999999992, 99.9999875393445), (89.8999999999992, 99.9999877885575), (89.9999999999992, 99.9999880327864), (90.0999999999992, 99.9999882721306), (90.1999999999992, 99.9999885066880), (90.2999999999991, 99.9999887365542), (90.3999999999991, 99.9999889618231), (90.4999999999991, 99.9999891825866), (90.5999999999991, 99.9999893989348), (90.6999999999991, 99.9999896109561), (90.7999999999991, 99.9999898187370), (90.8999999999991, 99.9999900223622), (90.9999999999991, 99.9999902219149), (91.0999999999991, 99.9999904174766), (91.1999999999991, 99.9999906091271), (91.2999999999991, 99.9999907969445), (91.3999999999991, 99.9999909810056), (91.4999999999991, 99.9999911613855), (91.5999999999991, 99.9999913381577), (91.6999999999991, 99.9999915113946), (91.7999999999991, 99.9999916811666), (91.8999999999991, 99.9999918475433), (91.9999999999990, 99.9999920105924), (92.0999999999990, 99.9999921703806), (92.1999999999990, 99.9999923269729), (92.2999999999990, 99.9999924804335), (92.3999999999990, 99.9999926308248), (92.4999999999990, 99.9999927782083), (92.5999999999990, 99.9999929226441), (92.6999999999990, 99.9999930641912), (92.7999999999990, 99.9999932029074), (92.8999999999990, 99.9999933388492), (92.9999999999990, 99.9999934720722), (93.0999999999990, 99.9999936026308), (93.1999999999990, 99.9999937305782), (93.2999999999990, 99.9999938559666), (93.3999999999990, 99.9999939788472), (93.4999999999990, 99.9999940992703), (93.5999999999990, 99.9999942172849), (93.6999999999990, 99.9999943329392), (93.7999999999989, 99.9999944462804), (93.8999999999989, 99.9999945573548), (93.9999999999989, 99.9999946662077), (94.0999999999989, 99.9999947728835), (94.1999999999989, 99.9999948774258), (94.2999999999989, 99.9999949798773), (94.3999999999989, 99.9999950802798), (94.4999999999989, 99.9999951786742), (94.5999999999989, 99.9999952751007), (94.6999999999989, 99.9999953695987), (94.7999999999989, 99.9999954622067), (94.8999999999989, 99.9999955529625), (94.9999999999989, 99.9999956419033), (95.0999999999989, 99.9999957290652), (95.1999999999989, 99.9999958144839), (95.2999999999989, 99.9999958981942), (95.3999999999989, 99.9999959802304), (95.4999999999988, 99.9999960606257), (95.5999999999988, 99.9999961394132), (95.6999999999988, 99.9999962166250), (95.7999999999988, 99.9999962922925), (95.8999999999988, 99.9999963664466), (95.9999999999988, 99.9999964391177), (96.0999999999988, 99.9999965103353), (96.1999999999988, 99.9999965801286), (96.2999999999988, 99.9999966485260), (96.3999999999988, 99.9999967155555), (96.4999999999988, 99.9999967812444), (96.5999999999988, 99.9999968456195), (96.6999999999988, 99.9999969087071), (96.7999999999988, 99.9999969705330), (96.8999999999988, 99.9999970311223), (96.9999999999988, 99.9999970904999), (97.0999999999988, 99.9999971486899), (97.1999999999988, 99.9999972057161), (97.2999999999987, 99.9999972616018), (97.3999999999987, 99.9999973163697), (97.4999999999987, 99.9999973700423), (97.5999999999987, 99.9999974226415), (97.6999999999987, 99.9999974741887), (97.7999999999987, 99.9999975247049), (97.8999999999987, 99.9999975742108), (97.9999999999987, 99.9999976227266), (98.0999999999987, 99.9999976702720), (98.1999999999987, 99.9999977168666), (98.2999999999987, 99.9999977625293), (98.3999999999987, 99.9999978072787), (98.4999999999987, 99.9999978511331), (98.5999999999987, 99.9999978941105), (98.6999999999987, 99.9999979362282), (98.7999999999987, 99.9999979775037), (98.8999999999987, 99.9999980179536), (98.9999999999986, 99.9999980575945), (99.0999999999986, 99.9999980964426), (99.1999999999986, 99.9999981345138), (99.2999999999986, 99.9999981718235), (99.3999999999986, 99.9999982083870), (99.4999999999986, 99.9999982442193), (99.5999999999986, 99.9999982793349), (99.6999999999986, 99.9999983137482), (99.7999999999986, 99.9999983474732), (99.8999999999986, 99.9999983805238), (99.9999999999986, 99.9999984129133)]
#Exercise 6
def euler3(diff_eq, initial, h, tfinal):
steps=int(round(tfinal/h))
fcn(N)=N+h*diff_eq(N)
ex6out=iterate(fcn, steps, initial)
times=srange(0, tfinal, h)
Ex6=zip(times, ex6out)
return Ex6

N_prime(N)=0.2*N*(1-N/100)
h=0.1
out6=euler3(N_prime, 10, h, 100)

out6

[(0.000000000000000, 10), (0.100000000000000, 10.1800000000000), (0.200000000000000, 10.3628735200000), (0.300000000000000, 10.5486531608817), (0.400000000000000, 10.7373714073976), (0.500000000000000, 10.9290606065975), (0.600000000000000, 11.1237529455809), (0.700000000000000, 11.3214804285737), (0.800000000000000, 11.5222748533262), (0.900000000000000, 11.7261677868336), (1.00000000000000, 11.9331905403773), (1.10000000000000, 12.1433741438903), (1.20000000000000, 12.3567493196484), (1.30000000000000, 12.5733464552916), (1.40000000000000, 12.7931955761805), (1.50000000000000, 13.0163263170940), (1.60000000000000, 13.2427678932773), (1.70000000000000, 13.4725490708478), (1.80000000000000, 13.7056981365714), (1.90000000000000, 13.9422428670207), (2.00000000000000, 14.1822104971285), (2.10000000000000, 14.4256276881541), (2.20000000000000, 14.6725204950778), (2.30000000000000, 14.9229143334436), (2.40000000000000, 15.1768339456718), (2.50000000000000, 15.4343033668624), (2.60000000000000, 15.6953458901155), (2.70000000000000, 15.9599840313958), (2.80000000000000, 16.2282394939672), (2.90000000000000, 16.5001331324319), (3.00000000000000, 16.7756849164029), (3.10000000000000, 17.0549138938481), (3.20000000000000, 17.3378381541397), (3.30000000000000, 17.6244747908507), (3.40000000000000, 17.9148398643370), (3.50000000000000, 18.2089483641508), (3.60000000000000, 18.5068141713282), (3.70000000000000, 18.8084500206003), (3.80000000000000, 19.1138674625768), (3.90000000000000, 19.4230768259530), (4.00000000000000, 19.7360871797947), (4.10000000000000, 20.0529062959569), (4.20000000000000, 20.3735406116931), (4.30000000000000, 20.6979951925157), (4.40000000000000, 21.0262736953681), (4.50000000000000, 21.3583783321730), (4.60000000000000, 21.6943098338204), (4.70000000000000, 22.0340674146637), (4.80000000000000, 22.3776487375901), (4.90000000000000, 22.7250498797374), (5.00000000000000, 23.0762652989248), (5.10000000000000, 23.4312878008740), (5.20000000000000, 23.7901085072900), (5.30000000000000, 24.1527168248781), (5.40000000000000, 24.5191004153711), (5.50000000000000, 24.8892451666427), (5.60000000000000, 25.2631351649825), (5.70000000000000, 25.6407526686093), (5.80000000000000, 26.0220780824990), (5.90000000000000, 26.4070899346026), (5.99999999999999, 26.7957648535318), (6.09999999999999, 27.1880775477853), (6.19999999999999, 27.5840007865921), (6.29999999999999, 27.9835053824450), (6.39999999999999, 28.3865601753961), (6.49999999999999, 28.7931320191857), (6.59999999999999, 29.2031857692746), (6.69999999999999, 29.6166842728451), (6.79999999999999, 30.0335883608386), (6.89999999999999, 30.4538568420897), (6.99999999999999, 30.8774464996198), (7.09999999999999, 31.3043120891448), (7.19999999999999, 31.7344063398528), (7.29999999999999, 32.1676799575012), (7.39999999999999, 32.6040816298816), (7.49999999999999, 33.0435580346936), (7.59999999999999, 33.4860538498691), (7.69999999999999, 33.9315117663792), (7.79999999999999, 34.3798725035564), (7.89999999999999, 34.8310748269554), (7.99999999999999, 35.2850555687743), (8.09999999999999, 35.7417496508515), (8.19999999999999, 36.2010901102477), (8.29999999999999, 36.6630081274186), (8.39999999999999, 37.1274330569767), (8.49999999999999, 37.5942924610362), (8.59999999999999, 38.0635121451277), (8.69999999999999, 38.5350161966658), (8.79999999999998, 39.0087270259437), (8.89999999999998, 39.4845654096256), (8.99999999999998, 39.9624505367008), (9.09999999999998, 40.4423000568551), (9.19999999999998, 40.9240301312145), (9.29999999999998, 41.4075554854027), (9.39999999999998, 41.8927894648554), (9.49999999999998, 42.3796440923231), (9.59999999999998, 42.8680301274912), (9.69999999999998, 43.3578571286387), (9.79999999999998, 43.8490335162540), (9.89999999999998, 44.3414666385172), (9.99999999999998, 44.8350628385566), (10.1000000000000, 45.3297275233803), (10.2000000000000, 45.8253652343791), (10.3000000000000, 46.3218797192938), (10.4000000000000, 46.8191740055340), (10.5000000000000, 47.3171504747325), (10.6000000000000, 47.8157109384175), (10.7000000000000, 48.3147567146766), (10.8000000000000, 48.8141887056904), (10.9000000000000, 49.3139074760053), (11.0000000000000, 49.8138133314150), (11.1000000000000, 50.3138063983199), (11.2000000000000, 50.8137867034288), (11.3000000000000, 51.3136542536690), (11.4000000000000, 51.8133091161694), (11.5000000000000, 52.3126514981792), (11.6000000000000, 52.8115818267888), (11.7000000000000, 53.3100008283151), (11.8000000000000, 53.8078096072184), (11.9000000000000, 54.3049097244174), (12.0000000000000, 54.8012032748703), (12.1000000000000, 55.2965929642930), (12.2000000000000, 55.7909821848871), (12.3000000000000, 56.2842750899540), (12.4000000000000, 56.7763766672728), (12.5000000000000, 57.2671928111254), (12.6000000000000, 57.7566303928546), (12.7000000000000, 58.2445973298443), (12.8000000000000, 58.7310026528181), (12.9000000000000, 59.2157565713534), (13.0000000000000, 59.6987705375169), (13.1000000000000, 60.1799573075290), (13.2000000000000, 60.6592310013724), (13.3000000000000, 61.1365071602642), (13.4000000000000, 61.6117028019181), (13.5000000000000, 62.0847364735261), (13.6000000000000, 62.5555283023992), (13.7000000000000, 63.0240000442087), (13.8000000000000, 63.4900751287784), (13.9000000000000, 63.9536787033824), (14.0000000000000, 64.4147376735109), (14.1000000000000, 64.8731807410717), (14.2000000000000, 65.3289384400004), (14.3000000000000, 65.7819431692609), (14.4000000000000, 66.2321292232214), (14.5000000000000, 66.6794328193975), (14.6000000000000, 67.1237921235621), (14.7000000000000, 67.5651472722240), (14.8000000000000, 68.0034403924850), (14.9000000000000, 68.4386156192918), (15.0000000000000, 68.8706191101006), (15.1000000000000, 69.2993990569809), (15.2000000000000, 69.7249056961888), (15.3000000000000, 70.1470913152441), (15.4000000000000, 70.5659102575511), (15.5000000000000, 70.9813189246068), (15.6000000000000, 71.3932757758436), (15.7000000000000, 71.8017413261593), (15.8000000000000, 72.2066781411888), (15.9000000000000, 72.6080508303755), (16.0000000000000, 73.0058260379057), (16.1000000000000, 73.3999724315685), (16.2000000000000, 73.7904606896088), (16.3000000000000, 74.1772634856441), (16.4000000000000, 74.5603554717132), (16.5000000000000, 74.9397132595338), (16.6000000000000, 75.3153154000403), (16.7000000000000, 75.6871423612796), (16.8000000000000, 76.0551765047418), (16.9000000000000, 76.4194020602032), (17.0000000000000, 76.7798050991594), (17.1000000000000, 77.1363735069297), (17.2000000000000, 77.4890969535081), (17.3000000000000, 77.8379668632443), (17.4000000000000, 78.1829763834284), (17.5000000000000, 78.5241203518627), (17.6000000000000, 78.8613952634932), (17.7000000000000, 79.1947992361820), (17.8000000000000, 79.5243319756938), (17.9000000000000, 79.8499947399716), (18.0000000000000, 80.1717903027764), (18.1000000000000, 80.4897229167615), (18.2000000000000, 80.8037982760533), (18.3000000000000, 81.1140234784069), (18.4000000000000, 81.4204069870039), (18.5000000000000, 81.7229585919581), (18.6000000000000, 82.0216893715927), (18.7000000000000, 82.3166116535506), (18.8000000000000, 82.6077389757973), (18.9000000000000, 82.8950860475745), (19.0000000000000, 83.1786687103591), (19.1000000000000, 83.4585038988807), (19.2000000000000, 83.7346096022504), (19.3000000000000, 84.0070048252472), (19.4000000000000, 84.2757095498103), (19.5000000000000, 84.5407446967817), (19.6000000000000, 84.8021320879401), (19.7000000000000, 85.0598944083668), (19.8000000000000, 85.3140551691816), (19.9000000000000, 85.5646386706832), (20.0000000000000, 85.8116699659280), (20.1000000000000, 86.0551748247783), (20.2000000000000, 86.2951796984492), (20.3000000000000, 86.5317116845807), (20.4000000000000, 86.7647984928596), (20.5000000000000, 86.9944684112155), (20.6000000000000, 87.2207502726098), (20.7000000000000, 87.4436734224386), (20.8000000000000, 87.6632676865654), (20.9000000000000, 87.8795633399994), (21.0000000000000, 88.0925910762336), (21.1000000000000, 88.3023819772534), (21.2000000000000, 88.5089674842271), (21.3000000000000, 88.7123793688868), (21.4000000000000, 88.9126497056067), (21.5000000000000, 89.1098108441845), (21.6000000000000, 89.3038953833309), (21.7000000000000, 89.4949361448701), (21.8000000000000, 89.6829661486526), (21.9000000000000, 89.8680185881816), (22.0000000000000, 90.0501268069521), (22.1000000000000, 90.2293242755015), (22.2000000000000, 90.4056445691688), (22.3000000000000, 90.5791213465588), (22.4000000000000, 90.7497883287071), (22.5000000000000, 90.9176792789402), (22.6000000000001, 91.0828279834253), (22.7000000000001, 91.2452682324022), (22.8000000000001, 91.4050338020896), (22.9000000000001, 91.5621584372592), (23.0000000000001, 91.7166758344664), (23.1000000000001, 91.8686196259308), (23.2000000000001, 92.0180233640546), (23.3000000000001, 92.1649205065702), (23.4000000000001, 92.3093444023051), (23.5000000000001, 92.4513282775545), (23.6000000000001, 92.5909052230488), (23.7000000000001, 92.7281081815050), (23.8000000000001, 92.8629699357510), (23.9000000000001, 92.9955230974084), (24.0000000000001, 93.1258000961244), (24.1000000000001, 93.2538331693382), (24.2000000000001, 93.3796543525700), (24.3000000000001, 93.5032954702203), (24.4000000000001, 93.6247881268665), (24.5000000000001, 93.7441636990437), (24.6000000000001, 93.8614533274979), (24.7000000000001, 93.9766879098979), (24.8000000000001, 94.0898980939930), (24.9000000000001, 94.2011142712052), (25.0000000000001, 94.3103665706420), (25.1000000000001, 94.4176848535171), (25.2000000000001, 94.5230987079678), (25.3000000000001, 94.6266374442559), (25.4000000000001, 94.7283300903397), (25.5000000000001, 94.8282053878057), (25.6000000000001, 94.9262917881474), (25.7000000000001, 95.0226174493806), (25.8000000000001, 95.1172102329820), (25.9000000000001, 95.2100977011406), (26.0000000000001, 95.3013071143112), (26.1000000000001, 95.3908654290582), (26.2000000000001, 95.4787992961784), (26.3000000000001, 95.5651350590940), (26.4000000000001, 95.6498987525033), (26.5000000000001, 95.7331161012805), (26.6000000000001, 95.8148125196139), (26.7000000000001, 95.8950131103724), (26.8000000000001, 95.9737426646922), (26.9000000000001, 96.0510256617723), (27.0000000000001, 96.1268862688721), (27.1000000000001, 96.2013483414998), (27.2000000000001, 96.2744354237853), (27.3000000000001, 96.3461707490273), (27.4000000000001, 96.4165772404076), (27.5000000000001, 96.4856775118647), (27.6000000000001, 96.5534938691173), (27.7000000000001, 96.6200483108329), (27.8000000000001, 96.6853625299320), (27.9000000000001, 96.7494579150218), (28.0000000000001, 96.8123555519521), (28.1000000000001, 96.8740762254876), (28.2000000000001, 96.9346404210890), (28.3000000000001, 96.9940683267977), (28.4000000000001, 97.0523798352169), (28.5000000000001, 97.1095945455854), (28.6000000000001, 97.1657317659355), (28.7000000000001, 97.2208105153323), (28.8000000000001, 97.2748495261873), (28.9000000000001, 97.3278672466426), (29.0000000000001, 97.3798818430194), (29.1000000000001, 97.4309112023277), (29.2000000000001, 97.4809729348311), (29.3000000000001, 97.5300843766635), (29.4000000000001, 97.5782625924929), (29.5000000000001, 97.6255243782289), (29.6000000000002, 97.6718862637686), (29.7000000000002, 97.7173645157795), (29.8000000000002, 97.7619751405131), (29.9000000000002, 97.8057338866485), (30.0000000000002, 97.8486562481603), (30.1000000000002, 97.8907574672094), (30.2000000000002, 97.9320525370528), (30.3000000000002, 97.9725562049698), (30.4000000000002, 98.0122829752020), (30.5000000000002, 98.0512471119038), (30.6000000000002, 98.0894626421020), (30.7000000000002, 98.1269433586608), (30.8000000000002, 98.1637028232512), (30.9000000000002, 98.1997543693219), (31.0000000000002, 98.2351111050693), (31.1000000000002, 98.2697859164057), (31.2000000000002, 98.3037914699225), (31.3000000000002, 98.3371402158486), (31.4000000000002, 98.3698443909993), (31.5000000000002, 98.4019160217174), (31.6000000000002, 98.4333669268027), (31.7000000000002, 98.4642087204294), (31.8000000000002, 98.4944528150500), (31.9000000000002, 98.5241104242837), (32.0000000000002, 98.5531925657901), (32.1000000000002, 98.5817100641240), (32.2000000000002, 98.6096735535730), (32.3000000000002, 98.6370934809761), (32.4000000000002, 98.6639801085206), (32.5000000000002, 98.6903435165201), (32.6000000000002, 98.7161936061688), (32.7000000000002, 98.7415401022740), (32.8000000000002, 98.7663925559657), (32.9000000000002, 98.7907603473812), (33.0000000000002, 98.8146526883261), (33.1000000000002, 98.8380786249097), (33.2000000000002, 98.8610470401551), (33.3000000000002, 98.8835666565831), (33.4000000000002, 98.9056460387694), (33.5000000000002, 98.9272935958755), (33.6000000000002, 98.9485175841521), (33.7000000000002, 98.9693261094149), (33.8000000000002, 98.9897271294928), (33.9000000000002, 99.0097284566484), (34.0000000000002, 99.0293377599695), (34.1000000000002, 99.0485625677333), (34.2000000000002, 99.0674102697411), (34.3000000000002, 99.0858881196253), (34.4000000000002, 99.1040032371268), (34.5000000000002, 99.1217626103445), (34.6000000000002, 99.1391730979551), (34.7000000000002, 99.1562414314049), (34.8000000000002, 99.1729742170724), (34.9000000000002, 99.1893779384018), (35.0000000000002, 99.2054589580084), (35.1000000000002, 99.2212235197548), (35.2000000000002, 99.2366777507984), (35.3000000000002, 99.2518276636112), (35.4000000000002, 99.2666791579700), (35.5000000000002, 99.2812380229192), (35.6000000000002, 99.2955099387048), (35.7000000000002, 99.3095004786814), (35.8000000000002, 99.3232151111900), (35.9000000000002, 99.3366592014091), (36.0000000000002, 99.3498380131779), (36.1000000000002, 99.3627567107925), (36.2000000000002, 99.3754203607747), (36.3000000000002, 99.3878339336141), (36.4000000000002, 99.4000023054832), (36.5000000000002, 99.4119302599269), (36.6000000000003, 99.4236224895245), (36.7000000000003, 99.4350835975271), (36.8000000000003, 99.4463180994682), (36.9000000000003, 99.4573304247495), (37.0000000000003, 99.4681249182009), (37.1000000000003, 99.4787058416163), (37.2000000000003, 99.4890773752641), (37.3000000000003, 99.4992436193731), (37.4000000000003, 99.5092085955951), (37.5000000000003, 99.5189762484427), (37.6000000000003, 99.5285504467039), (37.7000000000003, 99.5379349848336), (37.8000000000003, 99.5471335843213), (37.9000000000003, 99.5561498950368), (38.0000000000003, 99.5649874965529), (38.1000000000003, 99.5736498994462), (38.2000000000003, 99.5821405465756), (38.3000000000003, 99.5904628143396), (38.4000000000003, 99.5986200139115), (38.5000000000003, 99.6066153924546), (38.6000000000003, 99.6144521343156), (38.7000000000003, 99.6221333621980), (38.8000000000003, 99.6296621383148), (38.9000000000003, 99.6370414655222), (39.0000000000003, 99.6442742884322), (39.1000000000003, 99.6513634945072), (39.2000000000003, 99.6583119151344), (39.3000000000003, 99.6651223266823), (39.4000000000003, 99.6717974515374), (39.5000000000003, 99.6783399591241), (39.6000000000003, 99.6847524669052), (39.7000000000003, 99.6910375413657), (39.8000000000003, 99.6971976989782), (39.9000000000003, 99.7032354071519), (40.0000000000003, 99.7091530851642), (40.1000000000003, 99.7149531050753), (40.2000000000003, 99.7206377926274), (40.3000000000003, 99.7262094281262), (40.4000000000003, 99.7316702473083), (40.5000000000003, 99.7370224421909), (40.6000000000003, 99.7422681619079), (40.7000000000003, 99.7474095135296), (40.8000000000003, 99.7524485628683), (40.9000000000003, 99.7573873352681), (41.0000000000003, 99.7622278163817), (41.1000000000003, 99.7669719529318), (41.2000000000003, 99.7716216534590), (41.3000000000003, 99.7761787890560), (41.4000000000003, 99.7806451940880), (41.5000000000003, 99.7850226669001), (41.6000000000003, 99.7893129705113), (41.7000000000003, 99.7935178332962), (41.8000000000003, 99.7976389496532), (41.9000000000003, 99.8016779806612), (42.0000000000003, 99.8056365547233), (42.1000000000003, 99.8095162681991), (42.2000000000003, 99.8133186860247), (42.3000000000003, 99.8170453423216), (42.4000000000003, 99.8206977409938), (42.5000000000003, 99.8242773563139), (42.6000000000003, 99.8277856334982), (42.7000000000003, 99.8312239892706), (42.8000000000003, 99.8345938124168), (42.9000000000003, 99.8378964643271), (43.0000000000003, 99.8411332795293), (43.1000000000003, 99.8443055662117), (43.2000000000003, 99.8474146067362), (43.3000000000003, 99.8504616581410), (43.4000000000003, 99.8534479526350), (43.5000000000003, 99.8563746980818), (43.6000000000003, 99.8592430784747), (43.7000000000004, 99.8620542544030), (43.8000000000004, 99.8648093635092), (43.9000000000004, 99.8675095209374), (44.0000000000004, 99.8701558197732), (44.1000000000004, 99.8727493314755), (44.2000000000004, 99.8752911062995), (44.3000000000004, 99.8777821737119), (44.4000000000004, 99.8802235427982), (44.5000000000004, 99.8826162026623), (44.6000000000004, 99.8849611228179), (44.7000000000004, 99.8872592535729), (44.8000000000004, 99.8895115264063), (44.9000000000004, 99.8917188543376), (45.0000000000004, 99.8938821322895), (45.1000000000004, 99.8960022374434), (45.2000000000004, 99.8980800295876), (45.3000000000004, 99.9001163514598), (45.4000000000004, 99.9021120290819), (45.5000000000004, 99.9040678720893), (45.6000000000004, 99.9059846740529), (45.7000000000004, 99.9078632127955), (45.8000000000004, 99.9097042507021), (45.9000000000004, 99.9115085350236), (46.0000000000004, 99.9132767981752), (46.1000000000004, 99.9150097580290), (46.2000000000004, 99.9167081182002), (46.3000000000004, 99.9183725683287), (46.4000000000004, 99.9200037843546), (46.5000000000004, 99.9216024287886), (46.6000000000004, 99.9231691509770), (46.7000000000004, 99.9247045873616), (46.8000000000004, 99.9262093617345), (46.9000000000004, 99.9276840854882), (47.0000000000004, 99.9291293578601), (47.1000000000004, 99.9305457661733), (47.2000000000004, 99.9319338860717), (47.3000000000004, 99.9332942817511), (47.4000000000004, 99.9346275061855), (47.5000000000004, 99.9359341013492), (47.6000000000004, 99.9372145984344), (47.7000000000004, 99.9384695180644), (47.8000000000004, 99.9396993705030), (47.9000000000004, 99.9409046558598), (48.0000000000004, 99.9420858642906), (48.1000000000004, 99.9432434761954), (48.2000000000004, 99.9443779624109), (48.3000000000004, 99.9454897844005), (48.4000000000004, 99.9465793944397), (48.5000000000004, 99.9476472357987), (48.6000000000004, 99.9486937429204), (48.7000000000004, 99.9497193415956), (48.8000000000004, 99.9507244491347), (48.9000000000004, 99.9517094745360), (49.0000000000004, 99.9526748186504), (49.1000000000004, 99.9536208743428), (49.2000000000004, 99.9545480266513), (49.3000000000004, 99.9554566529419), (49.4000000000004, 99.9563471230611), (49.5000000000004, 99.9572197994851), (49.6000000000004, 99.9580750374663), (49.7000000000004, 99.9589131851765), (49.8000000000004, 99.9597345838477), (49.9000000000004, 99.9605395679100), (50.0000000000004, 99.9613284651267), (50.1000000000004, 99.9621015967266), (50.2000000000004, 99.9628592775343), (50.3000000000004, 99.9636018160970), (50.4000000000004, 99.9643295148095), (50.5000000000004, 99.9650426700366), (50.6000000000004, 99.9657415722329), (50.7000000000005, 99.9664265060602), (50.8000000000005, 99.9670977505031), (50.9000000000005, 99.9677555789815), (51.0000000000005, 99.9684002594613), (51.1000000000005, 99.9690320545634), (51.2000000000005, 99.9696512216694), (51.3000000000005, 99.9702580130263), (51.4000000000005, 99.9708526758486), (51.5000000000005, 99.9714354524184), (51.6000000000005, 99.9720065801833), (51.7000000000005, 99.9725662918533), (51.8000000000005, 99.9731148154946), (51.9000000000005, 99.9736523746221), (52.0000000000005, 99.9741791882902), (52.1000000000005, 99.9746954711815), (52.2000000000005, 99.9752014336941), (52.3000000000005, 99.9756972820264), (52.4000000000005, 99.9761832182614), (52.5000000000005, 99.9766594404484), (52.6000000000005, 99.9771261426831), (52.7000000000005, 99.9775835151868), (52.8000000000005, 99.9780317443833), (52.9000000000005, 99.9784710129747), (53.0000000000005, 99.9789015000158), (53.1000000000005, 99.9793233809861), (53.2000000000005, 99.9797368278619), (53.3000000000005, 99.9801420091854), (53.4000000000005, 99.9805390901338), (53.5000000000005, 99.9809282325857), (53.6000000000005, 99.9813095951875), (53.7000000000005, 99.9816833334175), (53.8000000000005, 99.9820495996491), (53.9000000000005, 99.9824085432128), (54.0000000000005, 99.9827603104566), (54.1000000000005, 99.9831050448061), (54.2000000000005, 99.9834428868221), (54.3000000000005, 99.9837739742580), (54.4000000000005, 99.9840984421161), (54.5000000000005, 99.9844164227019), (54.6000000000005, 99.9847280456782), (54.7000000000005, 99.9850334381182), (54.8000000000005, 99.9853327245562), (54.9000000000005, 99.9856260270393), (55.0000000000005, 99.9859134651763), (55.1000000000005, 99.9861951561867), (55.2000000000005, 99.9864712149482), (55.3000000000005, 99.9867417540436), (55.4000000000005, 99.9870068838065), (55.5000000000005, 99.9872667123662), (55.6000000000005, 99.9875213456915), (55.7000000000005, 99.9877708876343), (55.8000000000005, 99.9880154399714), (55.9000000000005, 99.9882551024460), (56.0000000000005, 99.9884899728086), (56.1000000000005, 99.9887201468563), (56.2000000000005, 99.9889457184722), (56.3000000000005, 99.9891667796633), (56.4000000000005, 99.9893834205983), (56.5000000000005, 99.9895957296440), (56.6000000000005, 99.9898037934013), (56.7000000000005, 99.9900076967408), (56.8000000000005, 99.9902075228367), (56.9000000000005, 99.9904033532015), (57.0000000000005, 99.9905952677183), (57.1000000000005, 99.9907833446742), (57.2000000000005, 99.9909676607913), (57.3000000000005, 99.9911482912589), (57.4000000000005, 99.9913253097632), (57.5000000000005, 99.9914987885178), (57.6000000000005, 99.9916687982934), (57.7000000000005, 99.9918354084457), (57.8000000000006, 99.9919986869447), (57.9000000000006, 99.9921587004016), (58.0000000000006, 99.9923155140964), (58.1000000000006, 99.9924691920042), (58.2000000000006, 99.9926197968215), (58.3000000000006, 99.9927673899916), (58.4000000000006, 99.9929120317296), (58.5000000000006, 99.9930537810472), (58.6000000000006, 99.9931926957762), (58.7000000000006, 99.9933288325928), (58.8000000000006, 99.9934622470401), (58.9000000000006, 99.9935929935508), (59.0000000000006, 99.9937211254699), (59.1000000000006, 99.9938466950756), (59.2000000000006, 99.9939697536015), (59.3000000000006, 99.9940903512567), (59.4000000000006, 99.9942085372467), (59.5000000000006, 99.9943243597936), (59.6000000000006, 99.9944378661551), (59.7000000000006, 99.9945491026446), (59.8000000000006, 99.9946581146492), (59.9000000000006, 99.9947649466491), (60.0000000000006, 99.9948696422350), (60.1000000000006, 99.9949722441261), (60.2000000000006, 99.9950727941880), (60.3000000000006, 99.9951713334487), (60.4000000000006, 99.9952679021166), (60.5000000000006, 99.9953625395957), (60.6000000000006, 99.9954552845026), (60.7000000000006, 99.9955461746816), (60.8000000000006, 99.9956352472207), (60.9000000000006, 99.9957225384661), (61.0000000000006, 99.9958080840374), (61.1000000000006, 99.9958919188422), (61.2000000000006, 99.9959740770901), (61.3000000000006, 99.9960545923067), (61.4000000000006, 99.9961334973473), (61.5000000000006, 99.9962108244104), (61.6000000000006, 99.9962866050506), (61.7000000000006, 99.9963608701917), (61.8000000000006, 99.9964336501393), (61.9000000000006, 99.9965049745927), (62.0000000000006, 99.9965748726578), (62.1000000000006, 99.9966433728583), (62.2000000000006, 99.9967105031478), (62.3000000000006, 99.9967762909207), (62.4000000000006, 99.9968407630238), (62.5000000000006, 99.9969039457672), (62.6000000000006, 99.9969658649347), (62.7000000000006, 99.9970265457948), (62.8000000000006, 99.9970860131107), (62.9000000000006, 99.9971442911502), (63.0000000000006, 99.9972014036962), (63.1000000000006, 99.9972573740558), (63.2000000000006, 99.9973122250703), (63.3000000000006, 99.9973659791241), (63.4000000000006, 99.9974186581540), (63.5000000000006, 99.9974702836582), (63.6000000000006, 99.9975208767052), (63.7000000000006, 99.9975704579418), (63.8000000000006, 99.9976190476025), (63.9000000000006, 99.9976666655166), (64.0000000000006, 99.9977133311174), (64.1000000000006, 99.9977590634493), (64.2000000000006, 99.9978038811760), (64.3000000000006, 99.9978478025878), (64.4000000000006, 99.9978908456097), (64.5000000000006, 99.9979330278078), (64.6000000000006, 99.9979743663972), (64.7000000000006, 99.9980148782486), (64.8000000000006, 99.9980545798955), (64.9000000000006, 99.9980934875406), (65.0000000000006, 99.9981316170629), (65.1000000000006, 99.9981689840234), (65.2000000000006, 99.9982056036724), (65.3000000000006, 99.9982414909550), (65.4000000000006, 99.9982766605174), (65.5000000000006, 99.9983111267131), (65.6000000000005, 99.9983449036084), (65.7000000000005, 99.9983780049884), (65.8000000000005, 99.9984104443624), (65.9000000000005, 99.9984422349698), (66.0000000000005, 99.9984733897851), (66.1000000000005, 99.9985039215233), (66.2000000000005, 99.9985338426452), (66.3000000000005, 99.9985631653623), (66.4000000000005, 99.9985919016422), (66.5000000000005, 99.9986200632128), (66.6000000000005, 99.9986476615677), (66.7000000000005, 99.9986747079706), (66.8000000000005, 99.9987012134599), (66.9000000000005, 99.9987271888533), (67.0000000000005, 99.9987526447522), (67.1000000000005, 99.9987775915460), (67.2000000000005, 99.9988020394162), (67.3000000000005, 99.9988259983409), (67.4000000000004, 99.9988494780984), (67.5000000000004, 99.9988724882717), (67.6000000000004, 99.9988950382520), (67.7000000000004, 99.9989171372428), (67.8000000000004, 99.9989387942634), (67.9000000000004, 99.9989600181529), (68.0000000000004, 99.9989808175735), (68.1000000000004, 99.9990012010143), (68.2000000000004, 99.9990211767945), (68.3000000000004, 99.9990407530670), (68.4000000000004, 99.9990599378216), (68.5000000000004, 99.9990787388885), (68.6000000000004, 99.9990971639410), (68.7000000000004, 99.9991152204991), (68.8000000000004, 99.9991329159326), (68.9000000000004, 99.9991502574636), (69.0000000000004, 99.9991672521699), (69.1000000000003, 99.9991839069878), (69.2000000000003, 99.9992002287148), (69.3000000000003, 99.9992162240126), (69.4000000000003, 99.9992318994095), (69.5000000000003, 99.9992472613033), (69.6000000000003, 99.9992623159639), (69.7000000000003, 99.9992770695358), (69.8000000000003, 99.9992915280406), (69.9000000000003, 99.9993056973794), (70.0000000000003, 99.9993195833354), (70.1000000000003, 99.9993331915761), (70.2000000000003, 99.9993465276556), (70.3000000000003, 99.9993595970171), (70.4000000000003, 99.9993724049947), (70.5000000000003, 99.9993849568161), (70.6000000000003, 99.9993972576041), (70.7000000000003, 99.9994093123793), (70.8000000000003, 99.9994211260620), (70.9000000000002, 99.9994327034737), (71.0000000000002, 99.9994440493399), (71.1000000000002, 99.9994551682913), (71.2000000000002, 99.9994660648661), (71.3000000000002, 99.9994767435117), (71.4000000000002, 99.9994872085867), (71.5000000000002, 99.9994974643624), (71.6000000000002, 99.9995075150247), (71.7000000000002, 99.9995173646757), (71.8000000000002, 99.9995270173356), (71.9000000000002, 99.9995364769441), (72.0000000000002, 99.9995457473622), (72.1000000000002, 99.9995548323737), (72.2000000000002, 99.9995637356866), (72.3000000000002, 99.9995724609348), (72.4000000000002, 99.9995810116796), (72.5000000000002, 99.9995893914109), (72.6000000000002, 99.9995976035489), (72.7000000000001, 99.9996056514456), (72.8000000000001, 99.9996135383856), (72.9000000000001, 99.9996212675880), (73.0000000000001, 99.9996288422075), (73.1000000000001, 99.9996362653358), (73.2000000000001, 99.9996435400027), (73.3000000000001, 99.9996506691772), (73.4000000000001, 99.9996576557693), (73.5000000000001, 99.9996645026304), (73.6000000000001, 99.9996712125553), (73.7000000000001, 99.9996777882826), (73.8000000000001, 99.9996842324962), (73.9000000000001, 99.9996905478263), (74.0000000000001, 99.9996967368506), (74.1000000000001, 99.9997028020952), (74.2000000000001, 99.9997087460356), (74.3000000000001, 99.9997145710980), (74.4000000000000, 99.9997202796597), (74.5000000000000, 99.9997258740509), (74.6000000000000, 99.9997313565548), (74.7000000000000, 99.9997367294093), (74.8000000000000, 99.9997419948072), (74.9000000000000, 99.9997471548978), (75.0000000000000, 99.9997522117870), (75.1000000000000, 99.9997571675390), (75.2000000000000, 99.9997620241764), (75.3000000000000, 99.9997667836816), (75.4000000000000, 99.9997714479971), (75.5000000000000, 99.9997760190267), (75.6000000000000, 99.9997804986361), (75.7000000000000, 99.9997848886537), (75.8000000000000, 99.9997891908714), (75.9000000000000, 99.9997934070451), (76.0000000000000, 99.9997975388957), (76.1000000000000, 99.9998015881095), (76.1999999999999, 99.9998055563395), (76.2999999999999, 99.9998094452051), (76.3999999999999, 99.9998132562938), (76.4999999999999, 99.9998169911609), (76.5999999999999, 99.9998206513310), (76.6999999999999, 99.9998242382979), (76.7999999999999, 99.9998277535258), (76.8999999999999, 99.9998311984493), (76.9999999999999, 99.9998345744747), (77.0999999999999, 99.9998378829797), (77.1999999999999, 99.9998411253148), (77.2999999999999, 99.9998443028035), (77.3999999999999, 99.9998474167426), (77.4999999999999, 99.9998504684031), (77.5999999999999, 99.9998534590305), (77.6999999999999, 99.9998563898456), (77.7999999999999, 99.9998592620446), (77.8999999999998, 99.9998620767997), (77.9999999999998, 99.9998648352599), (78.0999999999998, 99.9998675385511), (78.1999999999998, 99.9998701877766), (78.2999999999998, 99.9998727840177), (78.3999999999998, 99.9998753283341), (78.4999999999998, 99.9998778217643), (78.5999999999998, 99.9998802653260), (78.6999999999998, 99.9998826600166), (78.7999999999998, 99.9998850068135), (78.8999999999998, 99.9998873066746), (78.9999999999998, 99.9998895605386), (79.0999999999998, 99.9998917693254), (79.1999999999998, 99.9998939339365), (79.2999999999998, 99.9998960552555), (79.3999999999998, 99.9998981341483), (79.4999999999998, 99.9999001714632), (79.5999999999998, 99.9999021680320), (79.6999999999997, 99.9999041246694), (79.7999999999997, 99.9999060421742), (79.8999999999997, 99.9999079213289), (79.9999999999997, 99.9999097629007), (80.0999999999997, 99.9999115676410), (80.1999999999997, 99.9999133362867), (80.2999999999997, 99.9999150695594), (80.3999999999997, 99.9999167681668), (80.4999999999997, 99.9999184328021), (80.5999999999997, 99.9999200641447), (80.6999999999997, 99.9999216628605), (80.7999999999997, 99.9999232296021), (80.8999999999997, 99.9999247650089), (80.9999999999997, 99.9999262697075), (81.0999999999997, 99.9999277443123), (81.1999999999997, 99.9999291894250), (81.2999999999997, 99.9999306056355), (81.3999999999997, 99.9999319935218), (81.4999999999996, 99.9999333536505), (81.5999999999996, 99.9999346865766), (81.6999999999996, 99.9999359928442), (81.7999999999996, 99.9999372729865), (81.8999999999996, 99.9999385275260), (81.9999999999996, 99.9999397569747), (82.0999999999996, 99.9999409618345), (82.1999999999996, 99.9999421425971), (82.2999999999996, 99.9999432997445), (82.3999999999996, 99.9999444337490), (82.4999999999996, 99.9999455450734), (82.5999999999996, 99.9999466341713), (82.6999999999996, 99.9999477014873), (82.7999999999996, 99.9999487474570), (82.8999999999996, 99.9999497725074), (82.9999999999996, 99.9999507770567), (83.0999999999996, 99.9999517615151), (83.1999999999995, 99.9999527262843), (83.2999999999995, 99.9999536717582), (83.3999999999995, 99.9999545983226), (83.4999999999995, 99.9999555063557), (83.5999999999995, 99.9999563962282), (83.6999999999995, 99.9999572683033), (83.7999999999995, 99.9999581229368), (83.8999999999995, 99.9999589604778), (83.9999999999995, 99.9999597812679), (84.0999999999995, 99.9999605856422), (84.1999999999995, 99.9999613739290), (84.2999999999995, 99.9999621464501), (84.3999999999995, 99.9999629035209), (84.4999999999995, 99.9999636454502), (84.5999999999995, 99.9999643725409), (84.6999999999995, 99.9999650850898), (84.7999999999995, 99.9999657833878), (84.8999999999995, 99.9999664677198), (84.9999999999994, 99.9999671383652), (85.0999999999994, 99.9999677955976), (85.1999999999994, 99.9999684396855), (85.2999999999994, 99.9999690708916), (85.3999999999994, 99.9999696894735), (85.4999999999994, 99.9999702956839), (85.5999999999994, 99.9999708897700), (85.6999999999994, 99.9999714719745), (85.7999999999994, 99.9999720425348), (85.8999999999994, 99.9999726016840), (85.9999999999994, 99.9999731496501), (86.0999999999994, 99.9999736866570), (86.1999999999994, 99.9999742129237), (86.2999999999994, 99.9999747286651), (86.3999999999994, 99.9999752340917), (86.4999999999994, 99.9999757294097), (86.5999999999994, 99.9999762148214), (86.6999999999993, 99.9999766905249), (86.7999999999993, 99.9999771567143), (86.8999999999993, 99.9999776135799), (86.9999999999993, 99.9999780613082), (87.0999999999993, 99.9999785000819), (87.1999999999993, 99.9999789300802), (87.2999999999993, 99.9999793514785), (87.3999999999993, 99.9999797644488), (87.4999999999993, 99.9999801691598), (87.5999999999993, 99.9999805657765), (87.6999999999993, 99.9999809544609), (87.7999999999993, 99.9999813353716), (87.8999999999993, 99.9999817086641), (87.9999999999993, 99.9999820744907), (88.0999999999993, 99.9999824330009), (88.1999999999993, 99.9999827843408), (88.2999999999993, 99.9999831286539), (88.3999999999993, 99.9999834660808), (88.4999999999992, 99.9999837967591), (88.5999999999992, 99.9999841208239), (88.6999999999992, 99.9999844384074), (88.7999999999992, 99.9999847496392), (88.8999999999992, 99.9999850546463), (88.9999999999992, 99.9999853535534), (89.0999999999992, 99.9999856464822), (89.1999999999992, 99.9999859335526), (89.2999999999992, 99.9999862148815), (89.3999999999992, 99.9999864905838), (89.4999999999992, 99.9999867607721), (89.5999999999992, 99.9999870255566), (89.6999999999992, 99.9999872850454), (89.7999999999992, 99.9999875393445), (89.8999999999992, 99.9999877885575), (89.9999999999992, 99.9999880327864), (90.0999999999992, 99.9999882721306), (90.1999999999992, 99.9999885066880), (90.2999999999991, 99.9999887365542), (90.3999999999991, 99.9999889618231), (90.4999999999991, 99.9999891825866), (90.5999999999991, 99.9999893989348), (90.6999999999991, 99.9999896109561), (90.7999999999991, 99.9999898187370), (90.8999999999991, 99.9999900223622), (90.9999999999991, 99.9999902219149), (91.0999999999991, 99.9999904174766), (91.1999999999991, 99.9999906091271), (91.2999999999991, 99.9999907969445), (91.3999999999991, 99.9999909810056), (91.4999999999991, 99.9999911613855), (91.5999999999991, 99.9999913381577), (91.6999999999991, 99.9999915113946), (91.7999999999991, 99.9999916811666), (91.8999999999991, 99.9999918475433), (91.9999999999990, 99.9999920105924), (92.0999999999990, 99.9999921703806), (92.1999999999990, 99.9999923269729), (92.2999999999990, 99.9999924804335), (92.3999999999990, 99.9999926308248), (92.4999999999990, 99.9999927782083), (92.5999999999990, 99.9999929226441), (92.6999999999990, 99.9999930641912), (92.7999999999990, 99.9999932029074), (92.8999999999990, 99.9999933388492), (92.9999999999990, 99.9999934720722), (93.0999999999990, 99.9999936026308), (93.1999999999990, 99.9999937305782), (93.2999999999990, 99.9999938559666), (93.3999999999990, 99.9999939788472), (93.4999999999990, 99.9999940992703), (93.5999999999990, 99.9999942172849), (93.6999999999990, 99.9999943329392), (93.7999999999989, 99.9999944462804), (93.8999999999989, 99.9999945573548), (93.9999999999989, 99.9999946662077), (94.0999999999989, 99.9999947728835), (94.1999999999989, 99.9999948774258), (94.2999999999989, 99.9999949798773), (94.3999999999989, 99.9999950802798), (94.4999999999989, 99.9999951786742), (94.5999999999989, 99.9999952751007), (94.6999999999989, 99.9999953695987), (94.7999999999989, 99.9999954622067), (94.8999999999989, 99.9999955529625), (94.9999999999989, 99.9999956419033), (95.0999999999989, 99.9999957290652), (95.1999999999989, 99.9999958144839), (95.2999999999989, 99.9999958981942), (95.3999999999989, 99.9999959802304), (95.4999999999988, 99.9999960606257), (95.5999999999988, 99.9999961394132), (95.6999999999988, 99.9999962166250), (95.7999999999988, 99.9999962922925), (95.8999999999988, 99.9999963664466), (95.9999999999988, 99.9999964391177), (96.0999999999988, 99.9999965103353), (96.1999999999988, 99.9999965801286), (96.2999999999988, 99.9999966485260), (96.3999999999988, 99.9999967155555), (96.4999999999988, 99.9999967812444), (96.5999999999988, 99.9999968456195), (96.6999999999988, 99.9999969087071), (96.7999999999988, 99.9999969705330), (96.8999999999988, 99.9999970311223), (96.9999999999988, 99.9999970904999), (97.0999999999988, 99.9999971486899), (97.1999999999988, 99.9999972057161), (97.2999999999987, 99.9999972616018), (97.3999999999987, 99.9999973163697), (97.4999999999987, 99.9999973700423), (97.5999999999987, 99.9999974226415), (97.6999999999987, 99.9999974741887), (97.7999999999987, 99.9999975247049), (97.8999999999987, 99.9999975742108), (97.9999999999987, 99.9999976227266), (98.0999999999987, 99.9999976702720), (98.1999999999987, 99.9999977168666), (98.2999999999987, 99.9999977625293), (98.3999999999987, 99.9999978072787), (98.4999999999987, 99.9999978511331), (98.5999999999987, 99.9999978941105), (98.6999999999987, 99.9999979362282), (98.7999999999987, 99.9999979775037), (98.8999999999987, 99.9999980179536), (98.9999999999986, 99.9999980575945), (99.0999999999986, 99.9999980964426), (99.1999999999986, 99.9999981345138), (99.2999999999986, 99.9999981718235), (99.3999999999986, 99.9999982083870), (99.4999999999986, 99.9999982442193), (99.5999999999986, 99.9999982793349), (99.6999999999986, 99.9999983137482), (99.7999999999986, 99.9999983474732), (99.8999999999986, 99.9999983805238)]
#Exercise 7

diff_eq1(N)=0.05*N
def euler4(diff_eq, initial, h, tfinal):
steps=int(round(tfinal/h))
times=srange(0,steps+h,h)
count=srange(0,steps) #his line added by Hannah
vals=[initial]
tlist=srange(0,tfinal,h)
for i in count:
vals.append(vals[i]+h*diff_eq(vals[i]))
return zip(tfinal, vals)

part1=euler4(diff_eq1, 10, 0.1, 100)
part2=euler4(diff_eq1, 10, 1, 100)
part3=euler4(diff_eq1, 10, 0.01, 100)