Chapter 3.3, Problem 76ES

Suppose that the population of oxygen-dependent bacteria in a pond is modeled by the equation

$P\left(t\right)=\frac{60}{5+7e^{-t}}$

where $P\left(t\right)$ is the population (in billions) $t$ days 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 over time. 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 $P^{\prime }\left(t\right)$ .