Question

Please hurry!

A health club charges new members a one-time start-up fee in addition to a monthly fee. The cost, in dollars, of the membership for x months is modeled by the function
f(x) = 80 + 30x

What does the 80 represent in the function? (Multiple Choice) (1 point)
The start-up fee
The monthly fee
The rate of change in the monthly fee
The total amount charged each month

How did you know your answer for part a? Write at least 2 complete sentences.
(2 points)

Another health club (we will call it club B) charges a monthly fee of $35 a month and has a one-time start up fee of $20. Write a function that models the cost, in dollars, of the membership at club B for x months. (2 points)


Explain why you wrote your equation in part c the way you did. Write at least 2 complete sentences. (2 points)


Elizabeth wants to join a health club for 8 months to get in shape for her wedding. Which club should she join? Either show work or explain why you chose that club.

Answer 1

A) Because the 80 is by itself that would be the start up fee.

B) We are told x is the number of months. Since the X is being multiplied by 30, we know that would be the total monthly cost. This is being added to the 80, which does not have an exponent, so we know this is a single cost, which would be the start up fee.

C) Copying the same format as the given equation above, change the numbers:

f(x) = 20 + 35x

D) I used the same format as the first equation, which meant replacing the start up cost from the original one ( 80) with the start up of the new one (20). Then I changed the monthly cost from the original one (30) with the monthly cost of the new one (35).

E) Replace x in each equation with 8 and calculate the cost of each:

80 + 30(8) = 80 + 240 = $320

20 + 35(8) = 20 + 280 = $300

The second club (club B) is the cheaper option for her.