Matlab - ass#3.docx

Matlab - ass#3.docx - Hoon Shin Math 20D Section: B52...

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Hoon Shin Math 20D Section: B52 Assignment #3 Exercise 3.1 a) y’ (t) = r*y(t) ∫y’ (t) / y(t) = ∫r Ln │y │= rt y = ce^(rt) y = A*exp(rt) b) >> r = log(6.51/6.12) r = 0.0618 Exercise 3.2 a) Year: 1980 >> P(-4) ans = 4.7801 Error: 1980 >> 100*(P(-4) - 4.78)/4.78 ans = 0.0012 Year: 2005 >> P(1) ans = 6.5100 Error: 2005 >> 100*(P(1)-6.51)/6.51 ans = 0 Year: 2015 >> P(3) ans = 7.3661 Error: 2015 >> 100*(P(3)-7.3)/7.3 ans = 0.9061
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b) Year: 2030 >> P(6) ans = 8.8660 Error: 2030 >> 100*(P(6) - 8.86)/8.86 ans = 0.0680 Year: 2050 >> P(10) ans = 11.3513 Error: 2050 >> 100*(P(10) - 11.35)/11.35 ans = 0.0118 As time increases, the accuracy increases which proves accuracy of the model. Since all the error values are less than 1, model is effective. Exercise 3.3 a) Year:2200 >> P(40) ans = 72.4326 0 5 10 15 20 25 30 35 40 0 10 20 30 40 50 60 70 80
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b) It is because the model does not contain every single factor that will affect the population growth such as death caused by age, murder, diseases etc…
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This note was uploaded on 10/29/2008 for the course MATH 20D taught by Professor Mohanty during the Fall '06 term at UCSD.

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Matlab - ass#3.docx - Hoon Shin Math 20D Section: B52...

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