Coyotes are one of the few species of North American animals with an expanding range. The future population $P$ of coyotes in a region of Mississippi can be modeled by the equation $P(t)=57+18 \ln (14 t+1)$, where $t$ is time in years. How long will it take for the population to reach 180 ? Round your answer to the nearest tenth, if necessary.
A) 66.2 years
B) 66.4 years
C) 66.5 years
D) 5718 years

Question

Quizplus · Accepted Answer

The correct answer is A.The population will reach 180 when $P(t)=180$. So, we can solve the equation $57+18 \ln (14 t+1)=180$ for $t$.$18 \ln (14 t+1)=123$$\ln (14 t+1)=6.833$$14 t+1=e^{6.833}$$14 t=e^{6.833}-1$$t=\frac{e^{6.833}-1}{14}$$t\approx 66.2$So, it will take about 66.2 years for the population to reach 180.

Coyotes Are One of the Few Species of North American PPP

Coyotes Are One of the Few Species of North American $P$