Quiz Solutions for Mathematics 172: Exponentially Growing Populations - Prof. Re Howard, Quizzes of Mathematics

Download Quiz Solutions for Mathematics 172: Exponentially Growing Populations - Prof. Re Howard and more Quizzes Mathematics in PDF only on Docsity! Mathematics 172 Quiz #5 You must show your work to get full credit. 1. Solve dN dt = .05N , N(0) = 75. 2. Find the doubling time for an exponentially growing population with intrinsic growth rate r = .1. Solution for 1. In genreal the solution to dN dt = rN is N(t) = N(0)ert. In our case this just becomes N(t) = 75e.05t. Solution for 2. If r = .1, then the equation is dN dt = .N which has solution N(t) = N(0)e.1t. To find the doubling time we need to solve N(0)e.1t = 2N(0). Canceling the N(0)’s and taling ln gives .1t = ln(2) and thus t = ln(2) .1 = 6.93147