Chapter 4.2, Problem 11E

Reminder Round all answers to two decimal places unless otherwise indicated.

Gray Wolves in Idaho The report cited in Example $4.6$ tells us that in $2009$, there were $870$ gray wolves in Idaho, but that the population declined by $19\%$ that year. For purposes of this problem, we assume that this $19\%$ annual rate of decrease continues.

a. Find an exponential model that gives the wolf population $W$ as function of the time $t$ in years since $2009$.

b. It is expected that the wolf population cannot recover if there are fewer than $20$ individuals. How long must this rate of decline continue for the wolf population to reach $20$?