Chapter 3, Problem 2CA

a.

To determine

To write a function that represents the given situation.

Answer to Problem 2CA

  $f(x)=42+2x$

Explanation of Solution

Given:

A car rental company charges an initial fee of $42 and a daily fee of $12.

Calculation:

The initial fee is $42.

Let the car be rented for $x$ days.

Then, the daily fee for $x$ days is $\$12\times x=\$12x$ .

Then, the total rental bill for $x$ days is $\$(42+12x)$ .

Let $f(x)$ be the total rental bill as it depends on the value of $x$ .

Then, a function to represent the given situation is $f(x)=42+2x$ .

b.

To determine

The number of days you rented the car.

Answer to Problem 2CA

The car was rented for 8 days.

Explanation of Solution

Given:

A car rental company charges an initial fee of $42 and a daily fee of $12. The bill is $138.

Calculation:

A function to represent the given situation is given by,

  $f(x)=42+2x\mathrm{.................................}(1)$

Here, $f(x)=138$

Putting, $f(x)=138$ in equation (1),

  $\begin{array}{l}f(x)=42+12x\\ \Rightarrow 138=42+12x\\ \Rightarrow 42+12x=138\end{array}$

  $\begin{array}{l}\Rightarrow 12x=138-42\\ \Rightarrow 12x=96\\ \Rightarrow x=\frac{96}{12}\\ \Rightarrow x=8\end{array}$

Thus, the car was rented for 8 days.