Math 1210 / Math 1190 Assessment 3 Solutions Guide (1) Jada is a biologist modeling the population of owls in a forest. According to her model, the population of owls P at time t is given by P(t) = 100 + 200e-0.2t where t = 0 is the start of Jada's study. (a) According to this model, how many owls are there at the start of Jada's study (t = 0)? P(0) = 100 + 200e-0.2(0) = 100 + 200e = 100 + 200 = 300 (b) According to this model, how long after the start of the study will the population of owls reach 150? Your answer may contain logarithms. We want t where P(t) = 150: 100 + 200e -0.21 = 150 200e-0.21 = 50 e 0.21 - 50 200 e-0.21 In (e-0.21) = In (1) -0.2t = In (4) t = In (4) 0.2 (c) Which of the following could be a graph of P(t)? It may help to first think about a related example, like the graph of f (t) = e-0.2t e-0.21 = (e-0.2)* = (#2) Since 1