## Precalculus (6th Edition) Blitzer

Published by Pearson

# Chapter 1 - Section 1.10 - Modeling with Functions - Exercise Set - Page 291: 1

#### Answer

See the explanation below.

#### Work Step by Step

(a) Consider the provided statement: A car rental agency charges $\$200$per week plus$\$0.15$ per mile to rent a car Thus, to express the weekly cost to rent the car, the linear function representing the weekly cost of renting a car will be of the form $f\left( x \right)=mx+b$. Suppose that traveling x miles will cost an equal amount in total for renting car from the agency per week. Therefore, the agency that charges $\$200$per week plus$\$0.15$ per mile fee will cost after traveling x miles and a week: $200+\left( 0.15 \right)x$. Thus, by above given conditions $f\left( x \right)=200+\left( 0.15 \right)x$ Hence, to express the weekly cost to rent a car: $f\left( x \right)=200+\left( 0.15 \right)x$. (b) Consider the provided statement “The weekly cost to rent the car was $\$320$and the car rental agency charges$\$200$ per week plus $\$0.15$per mile to rent a car.” Thus, to calculate the number of miles driven during the week use the linear function representing the weekly cost of renting a car of the form$f\left( x \right)=200+\left( 0.15 \right)x$from part (a). The weekly cost to rent the car was$\$320$. Therefore, from the above given condition. \begin{align} & f\left( x \right)=200+\left( 0.15 \right)x \\ & 320=200+0.15x \\ & 120=0.15x \\ & \frac{120}{0.15}=x \end{align} Further simplify, \begin{align} & x=\frac{120}{0.15} \\ & =800 \end{align} Hence, the miles driven during the week were: $800\text{ miles}$.

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