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Unformatted text preview: Calculus for the Life Science I MAT1330A , MAT1330B, MAT1330E Assignment 2 Due date: Sept. 30 Instructor (circle one): Jing Li , Catalin Rada , Frithjof Lutscher DGD (circle one): 1 , 2 , 3 , 4 Student Name (printed): Student ID Number: Question 1 A model for the change in population size of the zooplankton species Daphnia galeata men- dota in Base Line Lake in Michigan is given by N ( t ) = N e rt , where N ( t ) is the population size at time t , N is the initial size of the population and r is the intrinsic rate of growth . a ) If the initial size of the population is 200 and the size of the population after one week is 250, find the intrinsic rate of growth of this population. r = ln(5 / 4) = 0 . 22314 . . . We have N (1) = 250, N = 200 and t = 1. Thus, N ( t ) = N e rt yields 250 = 200 e r 5 4 = e r r = ln parenleftbigg 5 4 parenrightbigg . b ) If the size of the population is 2 . 5 times its initial size after 2 weeks, find the intrinsic rate of growth of this population.of growth of this population....
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