Chapter 8.3, Problem 36PPS

a.

To determine

To write an equation representing the miles to the gallon as a function to tank size.

Answer to Problem 36PPS

The required function is $g=\frac{440}{t}$ .

Explanation of Solution

Given information:

The given statement is:

“Lawanda’s car went $440\text{ miles}$ on one tank of gas.”

The number of miles to the gallon that the car gets is $g$ and the size of the gas tank is $t$ .

The equation representing the miles to the gallon as a function to tank size is:

  $g=\frac{440}{t}$

Hence, the required function is $g=\frac{440}{t}$ .

b.

To determine

To graph the function.

Explanation of Solution

Given information:

The given function is:

  $g=\frac{440}{t}$

Graph:

This represents a transformation of the graph of $f\left(x\right)=\frac{1}{x}$ .

  $a=440$ : The graph is expanded.

  $h=0$ : There is an asymptote at $t=0$ .

  $k=0$ : There is an asymptote at $g=0$ .

The graph of the function is:

  

Interpretation:

The domain of the graph is all real numbers not equal to $0$ and the range is all real numbers except $0$ .

c.

To determine

To find how many miles does the car get per gallon if it has a $15\text{-gallon}$ tank.

Answer to Problem 36PPS

The car will get $29\text{ miles}$ .

Explanation of Solution

Given information:

The given statement is:

“Lawanda’s car went $440\text{ miles}$ on one tank of gas.”

The function is $g=\frac{440}{t}$ .

Calculation:

The speed can be calculated by:

  $\begin{array}{l}g=\frac{440}{t}\\ g=\frac{\text{440}}{\text{15}}\left[\text{Substitute the value of }t\right]\\ g\approx 29\text{ miles}\end{array}$

Hence, the car will get $29\text{ miles}$ .