Certainly! Let's break down the solution step-by-step.
### Part (a)
First, identify the variables given in the equation [tex]\( m = 15 - 0.99s \)[/tex].
- The independent variable is the one that you change or control directly. In this equation, that would be [tex]\( s \)[/tex], which represents the number of songs bought.
- The dependent variable is the one that changes in response to the independent variable. Here, it's [tex]\( m \)[/tex], which represents the amount of money left on the gift card.
So, the independent variable is [tex]\( s \)[/tex], and the dependent variable is [tex]\( m \)[/tex].
### Part (b)
Now, let's analyze how the amount of money left on the card changes for each extra song Nadia buys.
1. Initial Amount on the Gift Card:
- Nadia starts with [tex]$15 on the gift card.
2. Cost Per Song:
- Each song costs $[/tex]0.99.
3. Calculating the Remaining Amount After Buying Songs:
- After 1 Song:
- If Nadia buys 1 song, the amount of money remaining on the card is calculated as follows:
[tex]\[
m = 15 - 0.99 \times 1 = 15 - 0.99 = 14.01 \, \text{dollars}
\][/tex]
- After 2 Songs:
- If Nadia buys 2 songs, the calculation would be:
[tex]\[
m = 15 - 0.99 \times 2 = 15 - 1.98 = 13.02 \, \text{dollars}
\][/tex]
4. Change in Amount for Each Additional Song:
- To see how the amount changes for each additional song, observe that each song costs [tex]$0.99. This amount is subtracted from the gift card balance for each song purchased.
- Therefore, the change in the amount of money left on the card for each extra song Nadia buys is $[/tex]0.99.
In summary:
- The independent variable is [tex]\( s \)[/tex].
- The dependent variable is [tex]\( m \)[/tex].
- The amount of money left on the card decreases by $0.99 for each extra song Nadia buys.
