Chapter 9.1, Problem 37STP

To determine

To write: An equation using function notation that gives total cost as a function of the number of songs downloaded. Also, calculate the amount of the total bill if she downloaded $15$ songs.

Answer to Problem 37STP

An equation to represent cost as a function of total songs downloaded is as follows:

  $c(x)=15+1.75x$

Cost of downloading $15$ songs is $\$41.25$ .

Explanation of Solution

Given information:

Amount Kaylee has to pay per month = $\$15$

Amount Kaylee pays per song = $\$1.75$

Calculation:

Let total cost of downloading songs per month be c.

Let number of songs Kaylee downloads in a month be x.

Amount Kaylee pays per song = $\$1.75$

Therefore, amount Kaylee pays for x songs = $\$1.75x$

An equation to represent cost as a function of total songs downloaded can be evaluated as follows:

Words $\text{Total cost = amount to be paid per month + amount on the number of songs}$

Function $c(x)=15+1.75x$

The total bill amount if Kaylee downloaded $15$ songs can be calculated as follows:

  $\begin{array}{l}c(x)=15+1.75x[\text{Write the function]}\\ c(15)=15+1.75(15)[\text{Replace }x\text{ with 15]}\\ c(15)=15+25.25[\text{Multiply]}\\ c(15)=41.25[\text{Add]}\end{array}$