Quiz Solution for Mathematics 172 - Exponential Growth of Weeds - Prof. Re Howard, Quizzes of Mathematics

Download Quiz Solution for Mathematics 172 - Exponential Growth of Weeds - Prof. Re Howard and more Quizzes Mathematics in PDF only on Docsity! Mathematics 172 Quiz #2 You must show your work to get full credit. A population of weeds in a lawn grows exponentially. If it starts with 3 weeds, and after two months has 12 weeds, than find (a) A formula for Nt, the number of weeds after t months, (b) the per-month grow rate r, and (c) the doubling time. Solution for (a) and (c): As it is exponential growth, it is the form Nt = N0(1 + r) t. We know that N0 = 3 and the formula becomes Nt = 3(1 + r) t. But we also know that N2 = 12, this gives 3(1 + r)2 = 12 that is (1 + r)2 = 4 and taking square roots gives (1 + r) = √ 4 = 2. Therefore we have Nt = 3(2) t and r = 1. Solution for (b): To find the doubling time we need to solve Nt = 2N0 for t. In out case this becomes 3(2)t = (2)(3). That is 2t = 2 which clearly has the solution tdoubling = 1.