CoCalc Shared FilesLab 4 / Lab4-turnin.sagews
Author: Ashley Takenami
Views : 61
# Lab 1: Ashley Takenami

# Name:
# I worked on this code with:

# Please do all of your work for this week's lab in this worksheet. If
# you wish to create other worksheets for scratch work, you can, but
# this is the one that will be graded. You do not need to do anything
# to turn in your lab. It will be collected by your TA at the beginning
# of (or right before) next week’s lab.

# Be sure to clearly label which question you are answering as you go and to
# use enough comments that you and the grader can understand your code.


#1
#use initial value to get N'
#multiply N' by step size (delta T)
#add this value to initial N
#use sum as new initial value
#repeat steps 1-4

#2, #1
h=0.1
nprime(n)=0.2*n*(1-(n/100))
nprime(n)= nprime(n)*h+n
nprime(10)

10.1800000000000
#2, #2
n_list=[10]
nprime(n)=0.2*n*(1-(n/100))
count=srange(0,1000)
for i in count:
a= nprime(n_list[i])
b= a*0.1
c= n_list[i]+b
n_list.append(c)

n_list

[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, 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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]
n_list[-1] #The population value at t=100 is approximately 100

99.9999999911330
#3
n_list=[15]
nprime(n)=0.2*n*(1-(n/100))
count=srange(0,1000)
for i in count:
a= nprime(n_list[i])
b= a*0.1
c= n_list[i]+b
n_list.append(c)
n_list

[15, 15.2550000000000, 15.5135569950000, 15.7756940447726, 16.0414334211492, 16.3107965723311, 16.5838040868130, 16.8604756569513, 17.1408300422146, 17.4248850321516, 17.7126574091179, 18.0041629108017, 18.2994161925940, 18.5984307898479, 18.9012190800760, 19.2077922451349, 19.5181602334511, 19.8323317223404, 20.1503140804782, 20.4721133305794, 20.7977341123470, 21.1271796457523, 21.4604516947106, 21.7975505312166, 22.1384749000088, 22.4832219838293, 22.8317873693510, 23.1841650138422, 23.5403472126412, 23.9003245675157, 24.2640859559795, 24.6316185016433, 25.0029075456740, 25.3779366194400, 25.7566874184167, 26.1391397774311, 26.5252716473189, 26.9150590730724, 27.3084761735525, 27.7054951228392, 28.1060861332957, 28.5102174404152, 28.9178552895235, 29.3289639244048, 29.7435055779171, 30.1614404646627, 30.5827267757753, 31.0073206758825, 31.4351763023007, 31.8662457665154, 32.3004791579953, 32.7378245503880, 33.1782280101373, 33.6216336075616, 34.0679834304246, 34.5172176000299, 34.9692742898610, 35.4240897467863, 35.8815983148443, 36.3417324616156, 36.8044228071856, 37.2695981556953, 37.7371855294718, 38.2071102057241, 38.6792957557841, 39.1536640868671, 39.6301354863190, 40.1086286683126, 40.5890608229483, 41.0713476677095, 41.5554035012153, 42.0411412592098, 42.5284725727187, 43.0173078282994, 43.5075562303064, 43.9991258650859, 44.4919237670093, 44.9858559862516, 45.4808276582134, 45.9767430744825, 46.4735057552248, 46.9710185228931, 47.4691835771353, 47.9679025707821, 48.4670766867897, 48.9666067160129, 49.4663931356770, 49.9663361884199, 50.4663359617694, 50.9662924679236, 51.4661057236969, 51.9656758304983, 52.4649030542041, 52.9636879047908, 53.4619312155914, 53.9595342220431, 54.4563986397920, 54.9524267420247, 55.4475214358976, 55.9415863379387, 56.4345258482965, 56.9262452237180, 57.4166506491382, 57.9056493077679, 58.3931494495724, 58.8790604580359, 59.3632929151124, 59.8457586642695, 60.3263708715345, 60.8050440844592, 61.2816942889258, 61.7562389637201, 62.2285971328056, 62.6986894152383, 63.1664380726654, 63.6317670543611, 64.0946020397563, 64.5548704784245, 65.0125016274957, 65.4674265864726, 65.9195783294310, 66.3688917345937, 66.8153036112699, 67.2587527241621, 67.6991798150433, 68.1365276218183, 68.5707408949829, 69.0017664115051, 69.4295529861537, 69.8540514803053, 70.2752148082688, 70.6929979411645, 71.1073579084059, 71.5182537968312, 71.9256467475382, 72.3294999504787, 72.7297786368710, 73.1264500694947, 73.5194835309314, 73.9088503098190, 74.2945236851915, 74.6764789089735, 75.0546931867045, 75.4291456565685, 75.7998173668039, 76.1666912515718, 76.5297521053608, 76.8889865560064, 77.2443830364046, 77.5959317549977, 77.9436246651124, 78.2874554332275, 78.6274194062501, 78.9635135778779, 79.2957365541227, 79.6240885180730, 79.9485711939677, 80.2691878106556, 80.5859430645123, 80.8988430818832, 81.2078953811234, 81.5131088342996, 81.8144936286191, 82.1120612276500, 82.4058243323923, 82.6957968422599, 82.9819938160299, 83.2644314328137, 83.5431269531041, 83.8180986799456, 84.0893659202803, 84.3569489465110, 84.6208689583283, 84.8811480448424, 85.1378091470572, 85.3908760207262, 85.6403731996233, 85.8863259592616, 86.1287602810907, 86.3677028172010, 86.6031808555610, 86.8352222858120, 87.0638555656429, 87.2891096877647, 87.5110141475035, 87.7295989110287, 87.9448943842313, 88.1569313822652, 88.3657410997630, 88.5713550817362, 88.7738051951679, 88.9731236013053, 89.1693427286568, 89.3624952466978, 89.5526140402885, 89.7397321848045, 89.9238829219805, 90.1050996364669, 90.2834158330967, 90.4588651148603, 90.6314811615838, 90.8012977093070, 90.9683485303543, 91.1326674140934, 91.2942881483737, 91.4532445016375, 91.6095702056950, 91.7632989391545, 91.9144643114982, 92.0630998477943, 92.2092389740332, 92.3529150030797, 92.4941611212281, 92.6330103753487, 92.7694956606158, 92.9036497088031, 93.0355050771360, 93.1650941376871, 93.2924490673041, 93.4176018380550, 93.5405842081815, 93.6614277135435, 93.7801636595465, 93.8968231135352, 94.0114368976430, 94.1240355820839, 94.2346494788741, 94.3433086359704, 94.4500428318134, 94.5548815702634, 94.6578540759153, 94.7589892897822, 94.8583158653336, 94.9558621648788, 95.0516562562813, 95.1457259099945, 95.2380985964064, 95.3288014834827, 95.4178614346969, 95.5053050072367, 95.5911584504764, 95.6754477047051, 95.7581984001000, 95.8394358559354, 95.9191850800174, 95.9974707683348, 96.0743173049180, 96.1497487618952, 96.2237888997379, 96.2964611676884, 96.3677887043582, 96.4377943384918, 96.5065005898870, 96.5739296704635, 96.6401034854737, 96.7050436348465, 96.7687714146600, 96.8313078187326, 96.8926735403300, 96.9528889739780, 97.0119742173775, 97.0699490734144, 97.1268330522597, 97.1826453735525, 97.2374049686633, 97.2911304830286, 97.3438402785560, 97.3955524360917, 97.4462847579472, 97.4960547704808, 97.5448797267287, 97.5927766090829, 97.6397621320105, 97.6858527448116, 97.7310646344116, 97.7754137281847, 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99.2711512282905, 99.2856219596183, 99.2998074532290, 99.3137132502439, 99.3273447873385, 99.3407073985847, 99.3538063172661, 99.3666466776657, 99.3792335168262, 99.3915717762843, 99.4036663037780, 99.4155218549270, 99.4271430948880, 99.4385345999835, 99.4497008593047, 99.4606462762898, 99.4713751702761, 99.4818917780285, 99.4922002552420, 99.5023046780210, 99.5122090443339, 99.5219172754439, 99.5314332173167, 99.5407606420044, 99.5499032490068, 99.5588646666096, 99.5676484532009, 99.5762580985649, 99.5846970251538, 99.5929685893385, 99.6010760826379, 99.6090227329268, 99.6168117056236, 99.6244461048573, 99.6319289746145, 99.6392632998663, 99.6464520076756, 99.6534979682855, 99.6604039961882, 99.6671728511753, 99.6738072393696, 99.6803098142388, 99.6866831775910, 99.6929298805530, 99.6990524245302, 99.7050532621510, 99.7109347981923, 99.7166993904903, 99.7223493508334, 99.7278869458402, 99.7333143978205, 99.7386338856220, 99.7438475454604, 99.7489574717352, 99.7539657178303, 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99.9738142130107, 99.9743377916113, 99.9748509040693, 99.9753537594925, 99.9758465628152, 99.9763295148812, 99.9768028125252, 99.9772666486528, 99.9777212123187, 99.9781666888035, 99.9786032596887, 99.9790311029308, 99.9794503929333, 99.9798613006174, 99.9802639934916, 99.9806586357197, 99.9810453881877, 99.9814244085685, 99.9817958513866, 99.9821598680806, 99.9825166070650, 99.9828662137899, 99.9832088308007, 99.9835445977960, 99.9838736516841, 99.9841961266386, 99.9845121541533, 99.9848218630956, 99.9851253797585, 99.9854228279124, 99.9857143288554, 99.9860000014622, 99.9862799622330, 99.9865543253404, 99.9868232026764, 99.9870867038973, 99.9873449364687, 99.9875980057092, 99.9878460148331, 99.9880890649926, 99.9883272553186, 99.9885606829617, 99.9887894431308, 99.9890136291329, 99.9892333324102, 99.9894486425778, 99.9896596474600, 99.9898664331262, 99.9900690839258, 99.9902676825227, 99.9904623099286, 99.9906530455366, 99.9908399671527, 99.9910231510284, 99.9912026718911, 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99.9998987600186, 99.9999007848161, 99.9999027691178, 99.9999047137336, 99.9999066194571, 99.9999084870662, 99.9999103173232, 99.9999121109751, 99.9999138687541, 99.9999155913775, 99.9999172795486, 99.9999189339562, 99.9999205552758, 99.9999221441690, 99.9999237012844, 99.9999252272575, 99.9999267227113, 99.9999281882560, 99.9999296244898, 99.9999310319990, 99.9999324113581, 99.9999337631300, 99.9999350878665, 99.9999363861084, 99.9999376583854, 99.9999389052169, 99.9999401271118, 99.9999413245689, 99.9999424980768, 99.9999436481146, 99.9999447751517, 99.9999458796481, 99.9999469620545, 99.9999480228129, 99.9999490623561, 99.9999500811084, 99.9999510794858, 99.9999520578956, 99.9999530167372, 99.9999539564020, 99.9999548772735, 99.9999557797277, 99.9999566641327, 99.9999575308497, 99.9999583802323, 99.9999592126273, 99.9999600283744, 99.9999608278066, 99.9999616112502, 99.9999623790249, 99.9999631314441, 99.9999638688150, 99.9999645914384, 99.9999652996094, 99.9999659936170, 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99.9999988112537, 99.9999988350287, 99.9999988583281, 99.9999988811615, 99.9999989035383, 99.9999989254675, 99.9999989469582, 99.9999989680190, 99.9999989886586, 99.9999990088855]
n_list[-1]

99.9999990088855
n_list=[95]
nprime(n)=0.2*n*(1-(n/100))
count=srange(0,1000)
for i in count:
a= nprime(n_list[i])
b= a*0.1
c= n_list[i]+b
n_list.append(c)
n_list

[95, 95.0950000000000, 95.1882881950000, 95.2798919170011, 95.3698381945981, 95.4581537510373, 95.5448650025467, 95.6299980569266, 95.7135787123916, 95.7956324566528, 95.8761844662318, 95.9552596059959, 96.0328824289050, 96.1090771759623, 96.1838677763586, 96.2572778478017, 96.3293306970240, 96.4000493204571, 96.4694564050690, 96.5375743293524, 96.6044251644604, 96.6700306754785, 96.7344123228284, 96.7975912637964, 96.8595883541777, 96.9204241500331, 96.9801189095493, 97.0386925949983, 97.0961648747889, 97.1525551256062, 97.2078824346316, 97.2621656018392, 97.3154231423640, 97.3676732889358, 97.4189339943744, 97.4692229341418, 97.5185575089476, 97.5669548474013, 97.6144318087104, 97.6610049854171, 97.7066907061731, 97.7515050385462, 97.7954637918570, 97.8385825200412, 97.8808765245359, 97.9223608571843, 97.9630503231591, 98.0029594838987, 98.0421026600561, 98.0804939344562, 98.1181471550600, 98.1550759379328, 98.1912936702152, 98.2268135130934, 98.2616484047680, 98.2958110634190, 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99.9997656670249, 99.9997703536734, 99.9997749465894, 99.9997794476475, 99.9997838586848, 99.9997881815018, 99.9997924178628, 99.9997965694969, 99.9998006380987, 99.9998046253288, 99.9998085328146, 99.9998123621509, 99.9998161149009, 99.9998197925961, 99.9998233967377, 99.9998269287967, 99.9998303902148, 99.9998337824047, 99.9998371067511, 99.9998403646108, 99.9998435573135, 99.9998466861623, 99.9998497524344, 99.9998527573811, 99.9998557022292, 99.9998585881804, 99.9998614164128, 99.9998641880807, 99.9998669043154, 99.9998695662256, 99.9998721748977, 99.9998747313964, 99.9998772367654, 99.9998796920271, 99.9998820981836, 99.9998844562172, 99.9998867670901, 99.9998890317458, 99.9998912511084, 99.9998934260839, 99.9998955575599, 99.9998976464065, 99.9998996934763, 99.9999016996048, 99.9999036656107, 99.9999055922967, 99.9999074804489, 99.9999093308382, 99.9999111442198, 99.9999129213339, 99.9999146629057, 99.9999163696461, 99.9999180422518, 99.9999196814054, 99.9999212877760, 99.9999228620192, 99.9999244047777, 99.9999259166810, 99.9999273983463, 99.9999288503783, 99.9999302733697, 99.9999316679013, 99.9999330345424, 99.9999343738506, 99.9999356863728, 99.9999369726445, 99.9999382331908, 99.9999394685262, 99.9999406791549, 99.9999418655711, 99.9999430282590, 99.9999441676932, 99.9999452843387, 99.9999463786513, 99.9999474510777, 99.9999485020556, 99.9999495320140, 99.9999505413732, 99.9999515305452, 99.9999524999339, 99.9999534499347, 99.9999543809356, 99.9999552933165, 99.9999561874497, 99.9999570637004, 99.9999579224260, 99.9999587639771, 99.9999595886972, 99.9999603969230, 99.9999611889842, 99.9999619652042, 99.9999627258998, 99.9999634713816, 99.9999642019537, 99.9999649179143, 99.9999656195558, 99.9999663071645, 99.9999669810209, 99.9999676414003, 99.9999682885721, 99.9999689228004, 99.9999695443443, 99.9999701534572, 99.9999707503879, 99.9999713353799, 99.9999719086722, 99.9999724704986, 99.9999730210884, 99.9999735606665, 99.9999740894530, 99.9999746076639, 99.9999751155105, 99.9999756132001, 99.9999761009360, 99.9999765789172, 99.9999770473387, 99.9999775063918, 99.9999779562639, 99.9999783971385, 99.9999788291957, 99.9999792526117, 99.9999796675593, 99.9999800742081, 99.9999804727238, 99.9999808632693, 99.9999812460038, 99.9999816210837, 99.9999819886619, 99.9999823488886, 99.9999827019108, 99.9999830478725, 99.9999833869150, 99.9999837191766, 99.9999840447931, 99.9999843638971, 99.9999846766191, 99.9999849830867, 99.9999852834249, 99.9999855777564, 99.9999858662012, 99.9999861488772, 99.9999864258996, 99.9999866973815, 99.9999869634339, 99.9999872241652, 99.9999874796818, 99.9999877300882, 99.9999879754864, 99.9999882159766, 99.9999884516571, 99.9999886826239, 99.9999889089714, 99.9999891307919, 99.9999893481761, 99.9999895612125, 99.9999897699883, 99.9999899745885, 99.9999901750967, 99.9999903715947, 99.9999905641628, 99.9999907528795, 99.9999909378219, 99.9999911190655, 99.9999912966842, 99.9999914707505, 99.9999916413354, 99.9999918085087, 99.9999919723385, 99.9999921328917, 99.9999922902339, 99.9999924444292, 99.9999925955406, 99.9999927436298, 99.9999928887572, 99.9999930309820, 99.9999931703624, 99.9999933069551, 99.9999934408160, 99.9999935719997, 99.9999937005597, 99.9999938265485, 99.9999939500175, 99.9999940710172, 99.9999941895968, 99.9999943058049, 99.9999944196888, 99.9999945312950, 99.9999946406691, 99.9999947478557, 99.9999948528986, 99.9999949558406, 99.9999950567238, 99.9999951555893, 99.9999952524775, 99.9999953474280, 99.9999954404794, 99.9999955316698, 99.9999956210364, 99.9999957086157, 99.9999957944433, 99.9999958785545, 99.9999959609834, 99.9999960417637, 99.9999961209284, 99.9999961985099, 99.9999962745397, 99.9999963490489, 99.9999964220679, 99.9999964936265, 99.9999965637540, 99.9999966324789, 99.9999966998293, 99.9999967658327, 99.9999968305161, 99.9999968939058, 99.9999969560277, 99.9999970169071, 99.9999970765690, 99.9999971350376, 99.9999971923368, 99.9999972484901, 99.9999973035203, 99.9999973574499, 99.9999974103009, 99.9999974620949, 99.9999975128530, 99.9999975625959, 99.9999976113440, 99.9999976591171, 99.9999977059348, 99.9999977518161, 99.9999977967798, 99.9999978408442, 99.9999978840273, 99.9999979263467, 99.9999979678198, 99.9999980084634, 99.9999980482941, 99.9999980873283, 99.9999981255817, 99.9999981630700, 99.9999981998086, 99.9999982358125, 99.9999982710962, 99.9999983056743, 99.9999983395608, 99.9999983727696, 99.9999984053142, 99.9999984372079, 99.9999984684637, 99.9999984990945, 99.9999985291126, 99.9999985585303, 99.9999985873597, 99.9999986156125, 99.9999986433003, 99.9999986704343, 99.9999986970256, 99.9999987230851, 99.9999987486234, 99.9999987736509, 99.9999987981779, 99.9999988222143, 99.9999988457700, 99.9999988688546, 99.9999988914775, 99.9999989136480, 99.9999989353750, 99.9999989566675, 99.9999989775342, 99.9999989979835, 99.9999990180238, 99.9999990376634, 99.9999990569101, 99.9999990757719, 99.9999990942564, 99.9999991123713, 99.9999991301239, 99.9999991475214, 99.9999991645710, 99.9999991812796, 99.9999991976540, 99.9999992137009, 99.9999992294269, 99.9999992448383, 99.9999992599416, 99.9999992747428, 99.9999992892479, 99.9999993034630, 99.9999993173937, 99.9999993310458, 99.9999993444249, 99.9999993575364, 99.9999993703857, 99.9999993829780, 99.9999993953184, 99.9999994074120, 99.9999994192638, 99.9999994308785, 99.9999994422609, 99.9999994534157, 99.9999994643474, 99.9999994750605, 99.9999994855593, 99.9999994958481, 99.9999995059311, 99.9999995158125, 99.9999995254962, 99.9999995349863, 99.9999995442866, 99.9999995534009, 99.9999995623328, 99.9999995710862, 99.9999995796645, 99.9999995880712, 99.9999995963098, 99.9999996043836, 99.9999996122959, 99.9999996200500, 99.9999996276490, 99.9999996350960, 99.9999996423941, 99.9999996495462, 99.9999996565553, 99.9999996634242, 99.9999996701557, 99.9999996767526, 99.9999996832175, 99.9999996895532, 99.9999996957621, 99.9999997018469, 99.9999997078099, 99.9999997136537, 99.9999997193807, 99.9999997249930, 99.9999997304932, 99.9999997358833, 99.9999997411657, 99.9999997463423, 99.9999997514155, 99.9999997563872, 99.9999997612594, 99.9999997660343, 99.9999997707136, 99.9999997752993, 99.9999997797933, 99.9999997841974, 99.9999997885135, 99.9999997927432, 99.9999997968884, 99.9999998009506, 99.9999998049316, 99.9999998088329, 99.9999998126563, 99.9999998164032, 99.9999998200751, 99.9999998236736, 99.9999998272001, 99.9999998306561, 99.9999998340430, 99.9999998373621, 99.9999998406149, 99.9999998438026, 99.9999998469265, 99.9999998499880, 99.9999998529883, 99.9999998559285, 99.9999998588099, 99.9999998616337, 99.9999998644010, 99.9999998671130, 99.9999998697708, 99.9999998723754, 99.9999998749279, 99.9999998774293, 99.9999998798807, 99.9999998822831, 99.9999998846374, 99.9999998869447, 99.9999998892058, 99.9999998914217, 99.9999998935932, 99.9999998957214, 99.9999998978069, 99.9999998998508, 99.9999999018538, 99.9999999038167, 99.9999999057404, 99.9999999076256, 99.9999999094730, 99.9999999112836, 99.9999999130579, 99.9999999147967, 99.9999999165008, 99.9999999181708, 99.9999999198074, 99.9999999214112, 99.9999999229830, 99.9999999245234, 99.9999999260329, 99.9999999275122, 99.9999999289620, 99.9999999303827, 99.9999999317751, 99.9999999331396, 99.9999999344768, 99.9999999357873, 99.9999999370715, 99.9999999383301, 99.9999999395635, 99.9999999407722, 99.9999999419568, 99.9999999431176, 99.9999999442553, 99.9999999453702, 99.9999999464628, 99.9999999475335, 99.9999999485829, 99.9999999496112, 99.9999999506190, 99.9999999516066, 99.9999999525745, 99.9999999535230, 99.9999999544525, 99.9999999553635, 99.9999999562562, 99.9999999571311, 99.9999999579885, 99.9999999588287, 99.9999999596521, 99.9999999604591, 99.9999999612499, 99.9999999620249, 99.9999999627844, 99.9999999635287, 99.9999999642581, 99.9999999649730, 99.9999999656735, 99.9999999663600, 99.9999999670328, 99.9999999676922, 99.9999999683383, 99.9999999689716, 99.9999999695921, 99.9999999702003, 99.9999999707963, 99.9999999713804, 99.9999999719528, 99.9999999725137, 99.9999999730634, 99.9999999736022, 99.9999999741301, 99.9999999746475, 99.9999999751546, 99.9999999756515, 99.9999999761385, 99.9999999766157, 99.9999999770834, 99.9999999775417, 99.9999999779909, 99.9999999784310, 99.9999999788624, 99.9999999792852, 99.9999999796995, 99.9999999801055, 99.9999999805034, 99.9999999808933, 99.9999999812754, 99.9999999816499, 99.9999999820169, 99.9999999823766, 99.9999999827290, 99.9999999830745, 99.9999999834130, 99.9999999837447, 99.9999999840698, 99.9999999843884, 99.9999999847007, 99.9999999850066, 99.9999999853065, 99.9999999856004, 99.9999999858884, 99.9999999861706, 99.9999999864472, 99.9999999867182, 99.9999999869839, 99.9999999872442, 99.9999999874993, 99.9999999877493, 99.9999999879943, 99.9999999882344, 99.9999999884698, 99.9999999887004, 99.9999999889263, 99.9999999891478, 99.9999999893649, 99.9999999895776, 99.9999999897860, 99.9999999899903, 99.9999999901905, 99.9999999903867, 99.9999999905790, 99.9999999907674, 99.9999999909520, 99.9999999911330] 99.9999999911330
n_list[-1]

99.9999999911330
n_list=[200]
nprime(n)=0.2*n*(1-(n/100))
count=srange(0,1000)
for i in count:
a= nprime(n_list[i])
b= a*0.1
c= n_list[i]+b
n_list.append(c)
n_list

[200, 196.000000000000, 192.236800000000, 188.690538545152, 185.343525448763, 182.179951472583, 179.185643558324, 176.347857458009, 173.655101241163, 171.096984428570, 168.664088501032, 166.347855321075, 164.140490633513, 162.034880313101, 160.024517431747, 158.103438544529, 156.266167859499, 154.507668173190, 152.823297631791, 151.208771524616, 149.660128437911, 148.173700197859, 146.746085115751, 145.374124118706, 144.054879408424, 142.785615340318, 141.563781257501, 140.386996049867, 139.253034238883, 138.159813414714, 137.105382874450, 136.087913329309, 135.105687565030, 134.157091953847, 133.240608728622, 132.354808940319, 131.498346029200, 130.669949948101, 129.868421783175, 129.092628823548, 128.341500036704, 127.614021911104, 126.909234631660, 126.226228557335, 125.564140973320, 124.922153093113, 124.299487288291, 123.695404526031, 123.109201996380, 122.540210913070, 121.987794473207, 121.451345962584, 120.930286994611, 120.424065871984, 119.932156061195, 119.454054770922, 118.989281626097, 118.537377430240, 118.097903009237, 117.670438130386, 117.254580491035, 116.849944771630, 116.456161748436, 116.072877461569, 115.699752434358, 115.336460940371, 114.982690314729, 114.638140306621, 114.302522470161, 113.975559590956, 113.656985145961, 113.346542794386, 113.043985897586, 112.749077066015, 112.461587731488, 112.181297743100, 111.907994985297, 111.641475016677, 111.381540728230, 111.128002019796, 110.880675493610, 110.639384163898, 110.403957181543, 110.174229572905, 109.950041991966, 109.731240484999, 109.517676267023, 109.309205509378, 109.105689137747, 108.906992640058, 108.712985883679, 108.523542941403, 108.338541925720, 108.157864830916, 107.981397382578, 107.809028894091, 107.640652129755, 107.476163174167, 107.315461307522, 107.158448886543, 107.005031230720, 106.855116513597, 106.708615658842, 106.565442240854, 106.425512389673, 106.288744699986, 106.155060144005, 106.024381988050, 105.896635712622, 105.771748935824, 105.649651339951, 105.530274601100, 105.413552321645, 105.299419965464, 105.187814795761, 105.078675815375, 104.971943709460, 104.867560790421, 104.765470945002, 104.665619583437, 104.567953590549, 104.472421278737, 104.378972342743, 104.287557816132, 104.198130029404, 104.110642569668, 104.025050241807, 103.941309031081, 103.859376067084, 103.779209589017, 103.700768912213, 103.624014395860, 103.548907411875, 103.475410314874, 103.403486413205, 103.333099940988, 103.264216031125, 103.196800689243, 103.130820768528, 103.066243945421, 103.003038696126, 102.941174273921, 102.880620687221, 102.821348678368, 102.763329703128, 102.706535910855, 102.650940125311, 102.596515826095, 102.543237130686, 102.491078777052, 102.440016106816, 102.390025048959, 102.341082104033, 102.293164328869, 102.246249321764, 102.200315208126, 102.155340626560, 102.111304715385, 102.068187099558, 102.025967877991, 101.984627611262, 101.944147309686, 101.904508421740, 101.865692822839, 101.827682804441, 101.790461063465, 101.754010692032, 101.718315167490, 101.683358342737, 101.649124436820, 101.615598025802, 101.582764033890, 101.550607724815, 101.519114693455, 101.488270857696, 101.458062450513, 101.428476012281, 101.399498383291, 101.371116696481, 101.343318370352, 101.316091102096, 101.289422860896, 101.263301881416, 101.237716657459, 101.212655935805, 101.188108710205, 101.164064215539, 101.140511922129, 101.117441530197, 101.094842964479, 101.072706368966, 101.051022101796, 101.029780730268, 101.008973025992, 100.988589960159, 100.968622698934, 100.949062598969, 100.929901203026, 100.911130235716, 100.892741599340, 100.874727369841, 100.857079792850, 100.839791279838, 100.822854404363, 100.806261898402, 100.790006648784, 100.774081693707, 100.758480219339, 100.743195556504, 100.728221177447, 100.713550692681, 100.699177847909, 100.685096521018, 100.671300719149, 100.657784575835, 100.644542348209, 100.631568414277, 100.618857270259, 100.606403527990, 100.594201912382, 100.582247258952, 100.570534511399, 100.559058719245, 100.547815035530, 100.536798714557, 100.526005109694, 100.515429671225, 100.505067944251, 100.494915566640, 100.484968267024, 100.475221862839, 100.465672258419, 100.456315443120, 100.447147489501, 100.438164551535, 100.429362862870, 100.420738735119, 100.412288556200, 100.404008788705, 100.395895968311, 100.387946702221, 100.380157667648, 100.372525610324, 100.365047343052, 100.357719744278, 100.350539756710, 100.343504385951, 100.336610699180, 100.329855823843, 100.323236946394, 100.316751311041, 100.310396218542, 100.304169025008, 100.298067140749, 100.292088029130, 100.286229205464, 100.280488235923, 100.274862736474, 100.269350371840, 100.263948854479, 100.258655943590, 100.253469444138, 100.248387205904, 100.243407122545, 100.238527130689, 100.233745209036, 100.229059377491, 100.224467696302, 100.219968265226, 100.215559222714, 100.211238745104, 100.207005045841, 100.202856374706, 100.198791017070, 100.194807293155, 100.190903557316, 100.187078197336, 100.183329633739, 100.179656319113, 100.176056737452, 100.172529403508, 100.169072862159, 100.165685687789, 100.162366483684, 100.159113881435, 100.155926540361, 100.152803146937, 100.149742414238, 100.146743081395, 100.143803913060, 100.140923698886, 100.138101253011, 100.135335413559, 100.132625042153, 100.129969023430, 100.127366264572, 100.124815694847, 100.122316265159, 100.119866947602, 100.117466735033, 100.115114640645, 100.112809697556, 100.110550958400, 100.108337494929, 100.106168397628, 100.104042775329, 100.101959754843, 100.099918480588, 100.097918114236, 100.095957834359, 100.094036836091, 100.092154330784, 100.090309545684, 100.088501723608, 100.086730122624, 100.084994015749, 100.083292690638, 100.081625449290, 100.079991607762, 100.078390495875, 100.076821456944, 100.075283847497, 100.073777037016, 100.072300407665, 100.070853354042, 100.069435282922, 100.068045613012, 100.066683774710, 100.065349209871, 100.064041371570, 100.062759723879, 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n_list[-1]

99.9999999911330
#The carrying capacity, k, is 100. When N(0)>k, N' will be negative. This is because we subtract N/100 from 1, and N/100 will be a value greater than 1 if N>100. As a result, the list values will approach 100 and decrease with each subsequent result.

#4
timesteps=srange(0,100,0.1)
timesteps

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49.5000000000004, 49.6000000000004, 49.7000000000004, 49.8000000000004, 49.9000000000004, 50.0000000000004, 50.1000000000004, 50.2000000000004, 50.3000000000004, 50.4000000000004, 50.5000000000004, 50.6000000000004, 50.7000000000005, 50.8000000000005, 50.9000000000005, 51.0000000000005, 51.1000000000005, 51.2000000000005, 51.3000000000005, 51.4000000000005, 51.5000000000005, 51.6000000000005, 51.7000000000005, 51.8000000000005, 51.9000000000005, 52.0000000000005, 52.1000000000005, 52.2000000000005, 52.3000000000005, 52.4000000000005, 52.5000000000005, 52.6000000000005, 52.7000000000005, 52.8000000000005, 52.9000000000005, 53.0000000000005, 53.1000000000005, 53.2000000000005, 53.3000000000005, 53.4000000000005, 53.5000000000005, 53.6000000000005, 53.7000000000005, 53.8000000000005, 53.9000000000005, 54.0000000000005, 54.1000000000005, 54.2000000000005, 54.3000000000005, 54.4000000000005, 54.5000000000005, 54.6000000000005, 54.7000000000005, 54.8000000000005, 54.9000000000005, 55.0000000000005, 55.1000000000005, 55.2000000000005, 55.3000000000005, 55.4000000000005, 55.5000000000005, 55.6000000000005, 55.7000000000005, 55.8000000000005, 55.9000000000005, 56.0000000000005, 56.1000000000005, 56.2000000000005, 56.3000000000005, 56.4000000000005, 56.5000000000005, 56.6000000000005, 56.7000000000005, 56.8000000000005, 56.9000000000005, 57.0000000000005, 57.1000000000005, 57.2000000000005, 57.3000000000005, 57.4000000000005, 57.5000000000005, 57.6000000000005, 57.7000000000005, 57.8000000000006, 57.9000000000006, 58.0000000000006, 58.1000000000006, 58.2000000000006, 58.3000000000006, 58.4000000000006, 58.5000000000006, 58.6000000000006, 58.7000000000006, 58.8000000000006, 58.9000000000006, 59.0000000000006, 59.1000000000006, 59.2000000000006, 59.3000000000006, 59.4000000000006, 59.5000000000006, 59.6000000000006, 59.7000000000006, 59.8000000000006, 59.9000000000006, 60.0000000000006, 60.1000000000006, 60.2000000000006, 60.3000000000006, 60.4000000000006, 60.5000000000006, 60.6000000000006, 60.7000000000006, 60.8000000000006, 60.9000000000006, 61.0000000000006, 61.1000000000006, 61.2000000000006, 61.3000000000006, 61.4000000000006, 61.5000000000006, 61.6000000000006, 61.7000000000006, 61.8000000000006, 61.9000000000006, 62.0000000000006, 62.1000000000006, 62.2000000000006, 62.3000000000006, 62.4000000000006, 62.5000000000006, 62.6000000000006, 62.7000000000006, 62.8000000000006, 62.9000000000006, 63.0000000000006, 63.1000000000006, 63.2000000000006, 63.3000000000006, 63.4000000000006, 63.5000000000006, 63.6000000000006, 63.7000000000006, 63.8000000000006, 63.9000000000006, 64.0000000000006, 64.1000000000006, 64.2000000000006, 64.3000000000006, 64.4000000000006, 64.5000000000006, 64.6000000000006, 64.7000000000006, 64.8000000000006, 64.9000000000006, 65.0000000000006, 65.1000000000006, 65.2000000000006, 65.3000000000006, 65.4000000000006, 65.5000000000006, 65.6000000000005, 65.7000000000005, 65.8000000000005, 65.9000000000005, 66.0000000000005, 66.1000000000005, 66.2000000000005, 66.3000000000005, 66.4000000000005, 66.5000000000005, 66.6000000000005, 66.7000000000005, 66.8000000000005, 66.9000000000005, 67.0000000000005, 67.1000000000005, 67.2000000000005, 67.3000000000005, 67.4000000000004, 67.5000000000004, 67.6000000000004, 67.7000000000004, 67.8000000000004, 67.9000000000004, 68.0000000000004, 68.1000000000004, 68.2000000000004, 68.3000000000004, 68.4000000000004, 68.5000000000004, 68.6000000000004, 68.7000000000004, 68.8000000000004, 68.9000000000004, 69.0000000000004, 69.1000000000003, 69.2000000000003, 69.3000000000003, 69.4000000000003, 69.5000000000003, 69.6000000000003, 69.7000000000003, 69.8000000000003, 69.9000000000003, 70.0000000000003, 70.1000000000003, 70.2000000000003, 70.3000000000003, 70.4000000000003, 70.5000000000003, 70.6000000000003, 70.7000000000003, 70.8000000000003, 70.9000000000002, 71.0000000000002, 71.1000000000002, 71.2000000000002, 71.3000000000002, 71.4000000000002, 71.5000000000002, 71.6000000000002, 71.7000000000002, 71.8000000000002, 71.9000000000002, 72.0000000000002, 72.1000000000002, 72.2000000000002, 72.3000000000002, 72.4000000000002, 72.5000000000002, 72.6000000000002, 72.7000000000001, 72.8000000000001, 72.9000000000001, 73.0000000000001, 73.1000000000001, 73.2000000000001, 73.3000000000001, 73.4000000000001, 73.5000000000001, 73.6000000000001, 73.7000000000001, 73.8000000000001, 73.9000000000001, 74.0000000000001, 74.1000000000001, 74.2000000000001, 74.3000000000001, 74.4000000000000, 74.5000000000000, 74.6000000000000, 74.7000000000000, 74.8000000000000, 74.9000000000000, 75.0000000000000, 75.1000000000000, 75.2000000000000, 75.3000000000000, 75.4000000000000, 75.5000000000000, 75.6000000000000, 75.7000000000000, 75.8000000000000, 75.9000000000000, 76.0000000000000, 76.1000000000000, 76.1999999999999, 76.2999999999999, 76.3999999999999, 76.4999999999999, 76.5999999999999, 76.6999999999999, 76.7999999999999, 76.8999999999999, 76.9999999999999, 77.0999999999999, 77.1999999999999, 77.2999999999999, 77.3999999999999, 77.4999999999999, 77.5999999999999, 77.6999999999999, 77.7999999999999, 77.8999999999998, 77.9999999999998, 78.0999999999998, 78.1999999999998, 78.2999999999998, 78.3999999999998, 78.4999999999998, 78.5999999999998, 78.6999999999998, 78.7999999999998, 78.8999999999998, 78.9999999999998, 79.0999999999998, 79.1999999999998, 79.2999999999998, 79.3999999999998, 79.4999999999998, 79.5999999999998, 79.6999999999997, 79.7999999999997, 79.8999999999997, 79.9999999999997, 80.0999999999997, 80.1999999999997, 80.2999999999997, 80.3999999999997, 80.4999999999997, 80.5999999999997, 80.6999999999997, 80.7999999999997, 80.8999999999997, 80.9999999999997, 81.0999999999997, 81.1999999999997, 81.2999999999997, 81.3999999999997, 81.4999999999996, 81.5999999999996, 81.6999999999996, 81.7999999999996, 81.8999999999996, 81.9999999999996, 82.0999999999996, 82.1999999999996, 82.2999999999996, 82.3999999999996, 82.4999999999996, 82.5999999999996, 82.6999999999996, 82.7999999999996, 82.8999999999996, 82.9999999999996, 83.0999999999996, 83.1999999999995, 83.2999999999995, 83.3999999999995, 83.4999999999995, 83.5999999999995, 83.6999999999995, 83.7999999999995, 83.8999999999995, 83.9999999999995, 84.0999999999995, 84.1999999999995, 84.2999999999995, 84.3999999999995, 84.4999999999995, 84.5999999999995, 84.6999999999995, 84.7999999999995, 84.8999999999995, 84.9999999999994, 85.0999999999994, 85.1999999999994, 85.2999999999994, 85.3999999999994, 85.4999999999994, 85.5999999999994, 85.6999999999994, 85.7999999999994, 85.8999999999994, 85.9999999999994, 86.0999999999994, 86.1999999999994, 86.2999999999994, 86.3999999999994, 86.4999999999994, 86.5999999999994, 86.6999999999993, 86.7999999999993, 86.8999999999993, 86.9999999999993, 87.0999999999993, 87.1999999999993, 87.2999999999993, 87.3999999999993, 87.4999999999993, 87.5999999999993, 87.6999999999993, 87.7999999999993, 87.8999999999993, 87.9999999999993, 88.0999999999993, 88.1999999999993, 88.2999999999993, 88.3999999999993, 88.4999999999992, 88.5999999999992, 88.6999999999992, 88.7999999999992, 88.8999999999992, 88.9999999999992, 89.0999999999992, 89.1999999999992, 89.2999999999992, 89.3999999999992, 89.4999999999992, 89.5999999999992, 89.6999999999992, 89.7999999999992, 89.8999999999992, 89.9999999999992, 90.0999999999992, 90.1999999999992, 90.2999999999991, 90.3999999999991, 90.4999999999991, 90.5999999999991, 90.6999999999991, 90.7999999999991, 90.8999999999991, 90.9999999999991, 91.0999999999991, 91.1999999999991, 91.2999999999991, 91.3999999999991, 91.4999999999991, 91.5999999999991, 91.6999999999991, 91.7999999999991, 91.8999999999991, 91.9999999999990, 92.0999999999990, 92.1999999999990, 92.2999999999990, 92.3999999999990, 92.4999999999990, 92.5999999999990, 92.6999999999990, 92.7999999999990, 92.8999999999990, 92.9999999999990, 93.0999999999990, 93.1999999999990, 93.2999999999990, 93.3999999999990, 93.4999999999990, 93.5999999999990, 93.6999999999990, 93.7999999999989, 93.8999999999989, 93.9999999999989, 94.0999999999989, 94.1999999999989, 94.2999999999989, 94.3999999999989, 94.4999999999989, 94.5999999999989, 94.6999999999989, 94.7999999999989, 94.8999999999989, 94.9999999999989, 95.0999999999989, 95.1999999999989, 95.2999999999989, 95.3999999999989, 95.4999999999988, 95.5999999999988, 95.6999999999988, 95.7999999999988, 95.8999999999988, 95.9999999999988, 96.0999999999988, 96.1999999999988, 96.2999999999988, 96.3999999999988, 96.4999999999988, 96.5999999999988, 96.6999999999988, 96.7999999999988, 96.8999999999988, 96.9999999999988, 97.0999999999988, 97.1999999999988, 97.2999999999987, 97.3999999999987, 97.4999999999987, 97.5999999999987, 97.6999999999987, 97.7999999999987, 97.8999999999987, 97.9999999999987, 98.0999999999987, 98.1999999999987, 98.2999999999987, 98.3999999999987, 98.4999999999987, 98.5999999999987, 98.6999999999987, 98.7999999999987, 98.8999999999987, 98.9999999999986, 99.0999999999986, 99.1999999999986, 99.2999999999986, 99.3999999999986, 99.4999999999986, 99.5999999999986, 99.6999999999986, 99.7999999999986, 99.8999999999986]
list_plot(zip(timesteps,n_list), axes_labels=["t","N"])

list_plot((timesteps,n_list), axes_labels=["t","N"])
#The list_plot function won't work with two different lists unless we use the zip function. Using the zip function directs the computer to combine the lists into ordered pairs, which can be plotted.

3D rendering not yet implemented
#5
def N_prime(n,h,s,f):
vals=[n]
count=srange(0,s)
for i in count:
n_old=vals[i]
n_new=f(n_old)
vals.append(n_new)
return vals
N_prime(10,10,100, nprime(n))

[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]
#6
def N_prime(n,h,s,f):
vals=[n]
count=srange(0,s)
for i in count:
n_old=vals[i]
n_new=f(n_old)
vals.append(n_new)
return zip(count,vals)
N_prime(10,0.1,1000, nprime(n))

[(0, 10), (1, 10.1800000000000), (2, 10.3628735200000), (3, 10.5486531608817), (4, 10.7373714073976), (5, 10.9290606065975), (6, 11.1237529455809), (7, 11.3214804285737), (8, 11.5222748533262), (9, 11.7261677868336), (10, 11.9331905403773), (11, 12.1433741438903), (12, 12.3567493196484), (13, 12.5733464552916), (14, 12.7931955761805), (15, 13.0163263170940), (16, 13.2427678932773), (17, 13.4725490708478), (18, 13.7056981365714), (19, 13.9422428670207), (20, 14.1822104971285), (21, 14.4256276881541), (22, 14.6725204950778), (23, 14.9229143334436), (24, 15.1768339456718), (25, 15.4343033668624), (26, 15.6953458901155), (27, 15.9599840313958), (28, 16.2282394939672), (29, 16.5001331324319), (30, 16.7756849164029), (31, 17.0549138938481), (32, 17.3378381541397), (33, 17.6244747908507), (34, 17.9148398643370), (35, 18.2089483641508), (36, 18.5068141713282), (37, 18.8084500206003), (38, 19.1138674625768), (39, 19.4230768259530), (40, 19.7360871797947), (41, 20.0529062959569), (42, 20.3735406116931), (43, 20.6979951925157), (44, 21.0262736953681), (45, 21.3583783321730), (46, 21.6943098338204), (47, 22.0340674146637), (48, 22.3776487375901), (49, 22.7250498797374), (50, 23.0762652989248), (51, 23.4312878008740), (52, 23.7901085072900), (53, 24.1527168248781), (54, 24.5191004153711), (55, 24.8892451666427), (56, 25.2631351649825), (57, 25.6407526686093), (58, 26.0220780824990), (59, 26.4070899346026), (60, 26.7957648535318), (61, 27.1880775477853), (62, 27.5840007865921), (63, 27.9835053824450), (64, 28.3865601753961), (65, 28.7931320191857), (66, 29.2031857692746), (67, 29.6166842728451), (68, 30.0335883608386), (69, 30.4538568420897), (70, 30.8774464996198), (71, 31.3043120891448), (72, 31.7344063398528), (73, 32.1676799575012), (74, 32.6040816298816), (75, 33.0435580346936), (76, 33.4860538498691), (77, 33.9315117663792), (78, 34.3798725035564), (79, 34.8310748269554), (80, 35.2850555687743), (81, 35.7417496508515), (82, 36.2010901102477), (83, 36.6630081274186), (84, 37.1274330569767), (85, 37.5942924610362), (86, 38.0635121451277), (87, 38.5350161966658), (88, 39.0087270259437), (89, 39.4845654096256), (90, 39.9624505367008), (91, 40.4423000568551), (92, 40.9240301312145), (93, 41.4075554854027), (94, 41.8927894648554), (95, 42.3796440923231), (96, 42.8680301274912), (97, 43.3578571286387), (98, 43.8490335162540), (99, 44.3414666385172), (100, 44.8350628385566), (101, 45.3297275233803), (102, 45.8253652343791), (103, 46.3218797192938), (104, 46.8191740055340), (105, 47.3171504747325), (106, 47.8157109384175), (107, 48.3147567146766), (108, 48.8141887056904), (109, 49.3139074760053), (110, 49.8138133314150), (111, 50.3138063983199), (112, 50.8137867034288), (113, 51.3136542536690), (114, 51.8133091161694), (115, 52.3126514981792), (116, 52.8115818267888), (117, 53.3100008283151), (118, 53.8078096072184), (119, 54.3049097244174), (120, 54.8012032748703), (121, 55.2965929642930), (122, 55.7909821848871), (123, 56.2842750899540), (124, 56.7763766672728), (125, 57.2671928111254), (126, 57.7566303928546), (127, 58.2445973298443), (128, 58.7310026528181), (129, 59.2157565713534), (130, 59.6987705375169), (131, 60.1799573075290), (132, 60.6592310013724), (133, 61.1365071602642), (134, 61.6117028019181), (135, 62.0847364735261), (136, 62.5555283023992), (137, 63.0240000442087), (138, 63.4900751287784), (139, 63.9536787033824), (140, 64.4147376735109), (141, 64.8731807410717), (142, 65.3289384400004), (143, 65.7819431692609), (144, 66.2321292232214), (145, 66.6794328193975), (146, 67.1237921235621), (147, 67.5651472722240), (148, 68.0034403924850), (149, 68.4386156192918), (150, 68.8706191101006), (151, 69.2993990569809), (152, 69.7249056961888), (153, 70.1470913152441), (154, 70.5659102575511), (155, 70.9813189246068), (156, 71.3932757758436), (157, 71.8017413261593), (158, 72.2066781411888), (159, 72.6080508303755), (160, 73.0058260379057), (161, 73.3999724315685), (162, 73.7904606896088), (163, 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99.9999966485260), (964, 99.9999967155555), (965, 99.9999967812444), (966, 99.9999968456195), (967, 99.9999969087071), (968, 99.9999969705330), (969, 99.9999970311223), (970, 99.9999970904999), (971, 99.9999971486899), (972, 99.9999972057161), (973, 99.9999972616018), (974, 99.9999973163697), (975, 99.9999973700423), (976, 99.9999974226415), (977, 99.9999974741887), (978, 99.9999975247049), (979, 99.9999975742108), (980, 99.9999976227266), (981, 99.9999976702720), (982, 99.9999977168666), (983, 99.9999977625293), (984, 99.9999978072787), (985, 99.9999978511331), (986, 99.9999978941105), (987, 99.9999979362282), (988, 99.9999979775037), (989, 99.9999980179536), (990, 99.9999980575945), (991, 99.9999980964426), (992, 99.9999981345138), (993, 99.9999981718235), (994, 99.9999982083870), (995, 99.9999982442193), (996, 99.9999982793349), (997, 99.9999983137482), (998, 99.9999983474732), (999, 99.9999983805238)]
#7
def nprime_time(n,h,t_final,f):
vals=[n]
count=srange(0,t_final)
for i in count:
n_old=vals[i]
n_new=f(n_old)
vals.append(n_new)
return zip(count,vals)

#8
eulers_x(x)=x+(-2.1*x*h)
N_prime(1,1,10,eulers_x(x))

list_plot(N_prime(1,1,10,eulers_x(x)), plotjoined=true)

[(0, 1), (1, -1.10000000000000), (2, 1.21000000000000), (3, -1.33100000000000), (4, 1.46410000000000), (5, -1.61051000000000), (6, 1.77156100000000), (7, -1.94871710000000), (8, 2.14358881000000), (9, -2.35794769100000)]
#9
list_plot(N_prime(1,0.5,20,eulers_x(x)), plotjoined=true)

list_plot(N_prime(1,0.1,100,eulers_x(x)), plotjoined=true)