Chapter 7.5, Problem 47E

Hair Mousse Sales The amount of extremely popular hair mousse sold online at your website can be approximated by

$N\left(t\right)=\frac{80{\left(7\right)}^t}{20+7^t}\text{ million gallons per year}\text{.}$

( $t=0$ represents the current year.) Investigate the integrals ${\displaystyle {\int }_0^{+\infty }N\left(t\right)dt}$

and ${\displaystyle {\int }_{-\infty }^{0}N\left(t\right)dt}$, and interpret your answers.