Chapter 3, Problem 51RE

Suppose that the population of deer on an island is modeled by the equation

$P\left(t\right)=\frac{95}{5-4e^{-t/4}}$

where $P\left(t\right)$ is the number of deer $t$ weeks after an initial observation at time $t=0$ .

(a) Use a graphing utility to graph the function $P\left(t\right)$ .

(b) In words, explain what happens to the population overtime. Check your conclusion by finding ${\lim }_{t\to +\infty }P\left(t\right)$ .

(c) In words, what happens to the rate of population growth over time? Check your conclusion by graphing $P^{\prime }\left(t\right)$ .