Chapter 7.2, Problem 39PPS

(a)

To determine

To Find:

A function c(g) to represent the cost per gallon of gasoline.

Answer to Problem 39PPS

  $c(g)=2.95g$

Explanation of Solution

Given:

  

Calculation:

  $\begin{array}{l}\text{Let }\\ \text{number of gallons of gasoline = g}\\ \text{The price per gallon of gasolie = \$2}\text{.95}\\ Hence,\\ \text{The cost of gasoline can be represented by the }\\ \text{function:}\\ c(g)=2.95g\\ where,\\ \text{g is the number of gallons of gasoline}\text{.}\end{array}$

(b)

To determine

Use inverses to determine the function used to represent the cost per mile traveled in Leroy’s car.

Answer to Problem 39PPS

  $c(m)\approx 0.105m$

Explanation of Solution

Given:

The average miles traveled for every gallon g of gas consumed by Leroy’s car is represented by the function $m(g)=28g$ .

Calculation:

  $\begin{array}{l}\text{Given }\\ \text{The average miles traveled for every gallon g of }\\ \text{gas consumed by Leroy's car is :}\\ m(g)=28g\\ \Rightarrow g=\frac{m}{28}\mathrm{.........}\text{[divide each side by 28]}\\ From\text{ part (a), }\\ \text{Cost per gallon of gasoline is given by:}\\ c(g)=2.95g\\ \text{Substitute }g=\frac{m}{28}\text{ in the above equation :}\\ \Rightarrow c=2.95\times \frac{m}{28}\\ \Rightarrow \text{Cost per mile is given by:}\\ c(m)=2.95\times \frac{m}{28}\\ Hence,\\ c(m)\approx 0.105m\end{array}$