Logistic Population Growth Quiz Solutions for Mathematics 172 - Prof. Re Howard, Quizzes of Mathematics

Download Logistic Population Growth Quiz Solutions for Mathematics 172 - Prof. Re Howard and more Quizzes Mathematics in PDF only on Docsity! Mathematics 172 Quiz #8 You must show your work to get full credit. Consider a population growing logistically with a carry complicity of 100 and an intrinsic growth rate of r = .02 (individuals/year)/individual. (1) Write down the rate eqaution for this growth. Solution. dN dt = .02N ( 1− N K ) . where N is the number of individuals in the population at time t and t is time in years.  (2) If the population has size 150 at what rate is it changing? Solution. The rate of change is just the derivative dN dt , which is given by the rate equation above. So we just plug N = 150 into this equation dN dt ∣∣∣∣ N=150 = .02(150) ( 1− 150 100 ) = −1.5 individuals/year  (3) What is the per capita growth rate when N = 150? Solution. This is just the total growth rate divided by the population size. That is 1 N dN dt . In our case 1 N dN dt ∣∣∣∣ N=150 = 1 150 (−1.5) = −.01