Chapter 3.1, Problem 49AYU

(a)

To determine

To calculate: linear model that relates the cost $C,$ in dollars, of renting the truck to the number $x$ of miles driven.

Answer to Problem 49AYU

The linear model that relates the cost $C$ , of renting the truck to the number $x$ of miles driven is $C\left(x\right)=0.07x+29$ .

Explanation of Solution

Given information:

Per mile truck charges: $\$29$ plus $\$0.07$ per mile.

Calculation:

The fixed rental charge is $\$29$ which is the $y$ intercept of the cost function. For each mile driven, $7$ cents will be charged. This is the variable cost, which becomes the slope of the function.

  $\begin{array}{l}b=29\\ m=0.07\end{array}$

By putting $m$ and $b$ into the linear function to obtain the cost function.

  $C\left(x\right)=0.07x+29$

(a).

To determine

To calculate: The cost of renting the truck if the truck is driven $110$ miles and $230$ miles.

Answer to Problem 49AYU

The cost of renting truck is driven $110$ miles is $36.7$ dollars and $230$ miles is $45.1$ dollars.

Explanation of Solution

Given information:

Per mile truck charges: $\$29$ plus $\$0.07$ per mile.

Calculation:

Putting $m$ and $b$ into the linear function to obtain the cost function

  $C\left(x\right)=0.07x+29$

The costs of renting the truck are $C\left(110\right)$ and $C\left(230\right)$ respectively.

  $\begin{array}{l}C\left(110\right)=0.07\left(110\right)+29=36.7\\ C\left(230\right)=0.07\left(230\right)+29=45.1\end{array}$