A fitness center currently has 320 members. Monthly memberships fees are $45. The manager of the fitness center has determined that each time the membership increases by $5, approximately 10 members leave and go to a different gym.

Write a equation that can be used to find the revenue of the fitness center in dollars, y, after x price increases of $5

y = - 50x2 + 1,150x + 14,400

The revenue of the fitness center, y, is the product of two factors: the number of members and the fee paid by each member. There are 320 members now, but number of members goes down by 10 for each $5 increase in fees, so if x is the number of $5 price increases then members is equal to (320 - 10x). Since the fee is currently $45, and the fee increases by $5 for every price bump x, the fee is given by (45 + 5x). So, revenue y is given by y = (320 - 10x) (45 + 5x).