Question

Lexi received a $45 gift card to download music on her MP3 player. Each song costs $1.50. The amount left on the gift card is a function of the number of songs purchased. What is the domain and range?

Answer 1

Answer:

$A(n) = 45 - 1.5n$

The domain goes from 0 to 30

The range is from 0 to 45

Step-by-step explanation:

The amount left can be modeled by a first order function in the following format:

$A(n) = A_{0} - n*p$

In which $A(n)$ is her amount left, $A_{0}$ is her initial amount, n is the number of songs bought and p is the price of each song.

The problem states that Lexi received a $45 gift card. So her initial amount is 45. Each song costs $1.50, so $p = 1.50$. So, the function for the amount left on the gift card is:

$A(n) = 45 - 1.5n$

The range are the values that Lexi can have left. So the range is from 0 to 45.

The domain is the number of musics she can buy. So, the smallest value in the domain is 0. The biggest is the value of n for which $A(n) = 0$. So:

$A(n) = 45 - 1.5n$

$0 = 45 - 1.5n$

$1.5n = 45$

$n = \frac{45}{1.5}$

$n = 30$

The domain goes from 0 to 30