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

`A(n) = 45 - 1.5n`

The domain goes from 0 to 30

The range is from 0 to 45

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 = (45)/(1.5)`

`n = 30`

The domain goes from 0 to 30