Quiz Solutions for Mathematics 172: Population Growth with Discrete Logistic Model - Prof., Quizzes of Mathematics

Download Quiz Solutions for Mathematics 172: Population Growth with Discrete Logistic Model - Prof. and more Quizzes Mathematics in PDF only on Docsity! Mathematics 172 Quiz #12 You must show your work to get full credit. A population grows of wolves with a discrete logistic groth rate a per capita groth rate of r = 1.5 (wolves/year)/wolf and and a carrying capacity of K = 500. (a) If the population starts with 450 wolves, how many are the the next year? Solution: The growth equation is Nt+1 = Nt + 1.5Nt ( 1 + Nt 500 ) so letting N0 = 450 we get N1 = 450 + 1.5450 ( 1− 450 500 ) = 517.5 (b) Is the equilibrium point N = 500 stable? Solution: If 0 < r < 2, then the carrying capacity is stable. In our case r = 1.5, so it is stable. (c) Find the other zero of the equation. Solution: The is set Nt + 1.5Nt ( 1− Nt 500 ) = 0 and solve. This factors as Nt ( 1 + 1.5 ( 1− Nt 500 )) = 0 so one zero is Nt = 0 and the other is when 1 + 1.5 ( 1− Nt 500 ) = 0 Distributing the 1.5 1 + 1.5− 1.5Nt 500 = 0 So −1.5Nt 500 = −2.5 leading to Nt = (2.5)(500) 1.5 = 833.3333333 . . .