Problem: A museum currently charges $60 per year for memberships and they currently have 2,760 members. The management would like to increase the museum’s revenue from memberships, but they know if they raise the prices, some members may not renew. After market research, they estimate that the percentage of members who will renew if the membership price is raised by x dollars is:

where the percentage is expressed as a decimal (so an output of 0.3 means 30%)

1. If the museum raises the membership price by $15, how many members will renew?
   What is the annual revenue that the museum will receive?
2. Compute the annual revenue if the membership price is raised to $95.
3. Write an equation for the function that gives the annual revenue the museum will receive from memberships if they raise the fee by x dollars. Include a graph of your function.

4, Determine the price that the museum should charge in order to maximize the annual revenue from memberships. (I would recommend using your calculator or other technology for this rather than doing it by hand.)

5. Find the coordinates of the inflection point of the revenue function from part (3) ac-

curate to 2 decimal places. (Again, the calculator is recommended here.) Explain the

significance of the inflection point in this context.

Price: $6.74

Solution: The downloadable solution consists of 3 pages, 374 words and 1 charts.
Deliverable: Word Document