SharedLab 4 / Lab4-turnin.sagewsOpen in CoCalc
Author: Ashley Takenami
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# 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, 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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, 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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
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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, 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100.000000099504, 100.000000097514, 100.000000095563, 100.000000093652, 100.000000091779, 100.000000089943, 100.000000088145, 100.000000086382, 100.000000084654, 100.000000082961]
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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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))
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#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)