Matlab 3

Matlab 3 - MATLAB Assignment 3 Modeling with Differential...

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MATLAB Assignment 3 Modeling with Differential Equations Exercise 3.1 (a) (b) >> r=log(6.51/6.12) r = 0.0618 Exercise 3.2 (a) >> A=6.12 A = 6.1200 >> P='A*exp(r*t)' P = A*exp(r*t) >> P=subs(P) P = 153/25*exp(8903055811453881/144115188075855872*t) >> P=inline(char(P)) P =
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Inline function: P(t) = 153/25*exp(8903055811453881/144115188075855872*t) 1985 >> P(-3) ans = 5.0847 >> 100*(P(-3)-4.86)/4.86 ans = 4.6228 2005 >> P(1) ans = 6.5100 >> 100*(P(1)-6.51)/6.51 ans = 0 2015 >> P(3) ans = 7.3661 >> 100*(P(3)-7.30)/7.30 ans = 0.9061
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(b) 2035 >> P(7) ans = 9.4310 >> 100*(P(7)-8.59)/8.59 ans = 9.7906 2050 >> P(10) ans = 11.3513 >> 100*(P(10)-9.20)/9.20 ans = 23.3841 As the values for P(t) get larger, they stray farther from the UN population table and therefore have greater error values. This model is probably not as effective as it could be because it doesn’t take the carrying capacity into account. It seems to work best for the few years before 2000 until at least 15 years after 2000. Exercise 3.3 (a)
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0 5 10 15 20 25 30 35 40 0 10 20 30 40 50 60 70 80 t(40) = 72 billion people in the year 2200. (b)
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This note was uploaded on 04/20/2008 for the course MATH 20D taught by Professor Mohanty during the Winter '06 term at UCSD.

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Matlab 3 - MATLAB Assignment 3 Modeling with Differential...

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