If you are one of the first 100 people to join a new health club, you are charged a joining fee of $49. Otherwise, you are charged a joining fee of $149. The monthly membership cost is $38.75. a. Write an equation that gives the total cost (in dollars) of membership as a function of the number of months of membership if you are one of the first 100 members to join. b. Write an equation that gives the total cost (in dollars) of membership as a function of the number of months of membership if you are not one of the first 100 members to join. c. How are the graphs of these functions related? How do you know? d. After 6 months, what is the difference in total cost for a person who paid $149 to join and a person who paid $49 to join? after 12 months?

Question

Annika Hull

Mathematics

21 September, 17:42

If you are one of the first 100 people to join a new health club, you are charged a joining fee of $49. Otherwise, you are charged a joining fee of $149. The monthly membership cost is $38.75. a. Write an equation that gives the total cost (in dollars) of membership as a function of the number of months of membership if you are one of the first 100 members to join. b. Write an equation that gives the total cost (in dollars) of membership as a function of the number of months of membership if you are not one of the first 100 members to join. c. How are the graphs of these functions related? How do you know? d. After 6 months, what is the difference in total cost for a person who paid $149 to join and a person who paid $49 to join? after 12 months?

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Valentina Maldonado · Answer 1

a) Total cost = 49 + 38.75m

b) Total cost = 149 + 38.75m

c) The graphs of the lines are parallel and both has slope of - 2.5

d) Difference in total cost = $132.5

Step-by-step explanation:

Total cost, TC = Initial membership fee + monthly charges

a) TC = 49 + 38.75m

b) TC = 149 + 38.75m

d) 149 + 38.75 (6months) = 381.5

49 + 38.75 (12months) = 514

Difference in total cost = 514 - 381.5 = $132.5