Q. 49 - Precalculus Enhanced with Graphing Utilities

Question

Truck Rentals A truck rental company rents a truck for one day by charging \(29 plus \)0.07 per mile. 

(a) Write a linear model that relates the cost C, in dollars, of renting the truck to the number x of miles driven. 

(b) What is the cost of renting the truck if the truck is driven 110 miles? 230 miles? 

Step-by-Step Solution

Answer

Part (a) The linear model is $C\left(x\right)=0.07x+29$.

Part (b) The cost of renting the truck if the truck is driven 110 miles is $36.70 and for 230 miles $45.10.

Part (a) Step 1. Given Information.

The rents of a truck for one day is $29 plus $0.07 per mile. 

Part (a) Step 2. Explanation.

Find a linear model where the cost of renting the truck C in dollars, and x be number of miles driven. 

Rent per day is fix. This is y-intercept. so, $b=29$.

Charge per mile is slope. $m=0.07$.

So the function becomes $C\left(x\right)=0.07x+29$.

Part (b) Step 1. Explanation.

Find the cost of renting the truck if the truck is driven 110 miles.

We have $x=110$ Find C(x).

$$\begin{gathered} C\left(x\right)=0.07x+29 \\ =0.07\left(110\right)+29 \\ =36.70 \end{gathered}$$

The cost of renting the truck if the truck is driven 110 miles is $36.70.

Find the cost of renting the truck if the truck is driven 230 miles.

We have $x=230$, Find C(x).

$$\begin{gathered} C\left(x\right)=0.07x+29 \\ =0.07\left(230\right)+29 \\ =45.10 \end{gathered}$$

The cost of renting the truck if the truck is driven 230 miles is $45.10.