Chapter 3.3, Problem 75ES

Suppose that the percentage of U.S. households with broadband Internet access is modeled by the equation

$P\left(t\right)=\frac{5300}{53+47e^{-0.182t}}$

where $P\left(t\right)$ is the percentage $t$ years after an initial survey result made in the year $2007$ .

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

(b) In words, explain what happens to the percentage 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 $P^{\prime }\left(t\right)$ .