Question

.

Recall from a previous lesson that Kelly wants to add new music to her MP3 player. She was interested in a monthly
subscription site that offered its MP3 downloading service for a monthly subscription fee plus a fee per song. The
linear function that modeled the total monthly cost in dollars (y) based on the number of songs downloaded (x) is
y = 5.25 +0.30x.
The site has suddenly changed its monthly price structure. The linear function that models the new total monthly
cost in dollars (y) based on the number of songs downloaded (x) is y = 0.35x + 4.50.
a.
Explain the meaning of the value 4.50 in the new equation. Is this a better situation for Kelly than before?
b. Explain the meaning of the value 0.35 in the new equation. Is this a better situation for Kelly than before?
C.
If you were to graph the two equations (old versus new), which line would have the steeper slope? What does
this mean in the context of the problem?
d. Which subscription plan provides the better value if Kelly downloads fewer than 15 songs per month?

Answer 1

a) The value 4.50 in the new equation represents the monthly subscription fee, which is lower than the previous fee.

b) The value 0.35 in the new equation represents the fee per song downloaded, which is also lower than the previous fee.

c) The new equation has a steeper slope, indicating higher costs for each additional song in the new plan.

d) The old subscription plan provides the better value if Kelly downloads fewer than 15 songs per month.

Step-by-step explanation:

a. The value 4.50 in the new equation represents the monthly subscription fee for the site. It means that regardless of the number of songs downloaded, Kelly will need to pay $4.50 every month.

This is a better situation for Kelly than before because the new monthly fee is lower than the previous fee of $5.25.

b. The value 0.35 in the new equation represents the fee per song downloaded. It means that for each song Kelly downloads, she will need to pay $0.35.

This is a better situation for Kelly than before because the new fee per song is lower than the previous fee of $0.30.

c. The new equation, y = 0.35x + 4.50, has a steeper slope compared to the old equation, y = 5.25 + 0.30x.

This means that for each additional song downloaded, the total monthly cost increases at a faster rate in the new plan. In the context of the problem, the steeper slope indicates that Kelly will have to pay more for each additional song downloaded in the new plan.

d. If Kelly downloads fewer than 15 songs per month, the old subscription plan provides the better value.

This is because the total monthly cost in the old plan, y = 5.25 + 0.30x, is lower than the total monthly cost in the new plan, y = 0.35x + 4.50, for values of x less than 15.