Chapter 8, Problem 3RE

To determine

To determine the number billboards, present along a $100$ mile stretch off an interstate highway approaching a certain city .

Answer to Problem 3RE

There are total $1464$ billboards present along a $100$ mile stretch of an interstate highway approaching a certain city

Explanation of Solution

Given:

The number of billboards per mile along a $100$ mile stretch of an interstate highway approaching a certain city is modeled by the function $B\left(x\right)=21-e^{0.03x}$ , where $x$ is the distance from the city in miles.

Calculation:

Since , the number of billboards per mile along a $100$ mile stretch off an interstate highway approaching a certain city is given by

  $B\left(x\right)=21-e^{0.03x}$

  ${\displaystyle \underset{0}{\overset{100}{\int }}B\left(x\right)}={\displaystyle \underset{0}{\overset{100}{\int }}\left(21-e^{0.03x}\right)}dx={\left|21x-\frac{e^{0.03x}}{0.03}\right|}_0^{100}=\left(\left(21\times 100-\frac{e^{0.03\times 100}}{0.03}\right)-\left(0+\frac{1}{0.03}\right)\right)=1463.74\approx 1464$

Therefore, There are total $1464$ billboards present along a $100$ mile stretch ofan interstate highway approaching a certain city.