Question

An online shopping club has 14,000 members when it charges ​$9 per month for membership. For each ​$1 monthly increase in the membership​ fee, the club loses approximately 500 of its existing members. Write and simplify a function R to represent the monthly revenue received by the club when x represents the price increase.

​Hint: Monthly revenue​ = # membersmonthly fee.
PLEASE HELP

Answer 1

The monthly revenue received by the club can be calculated by multiplying the number of members by the membership fee. When considering an increase in the fee and corresponding loss of members, the revenue equation becomes (14,000 - 500x) * (9 + x) = 126,000 + 14,000x - 4,500x^2.

Step-by-step explanation:

The monthly revenue received by the club can be calculated by multiplying the number of members by the membership fee. Let's analyze the given information step by step:

With a membership fee of $9 per month, the club has 14,000 members. Therefore, the monthly revenue would be:

R = 14,000 * 9 = $126,000

Now, let's consider the effect of a monthly fee increase. For each $1 increase in the membership fee, the club loses approximately 500 members. So, for an increase of x dollars, the number of members decreases by 500x.

The new equation for monthly revenue would be:

R = (14,000 - 500x) * (9 + x) = 126,000 + 14,000x - 4,500x^2