Question

An online shopping club has 12,000 members when it charges $9 per month for membership. For each $1 monthly increase in membership fee, the club loses approximately 400 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 = # members. monthly fee.

Answer 1

The monthly revenue of the online shopping club can be represented by the function R(x) = (12,000 - (400 * x)) * (9 + x), where x is the price increase.

Step-by-step explanation:

The monthly revenue received by the club can be calculated by multiplying the number of members by the monthly fee.

Let's break down the steps to create the function R:

First, we know that the initial membership fee is $9 and the number of members is 12,000.

So the initial monthly revenue is $9 * 12,000 = $108,000.

Next, we need to account for the decrease in membership for each $1 increase in fee.

We know that for each $1 increase, the club loses approximately 400 members.

So if the fee increases by x dollars, the number of members remaining is 12,000 - (400 * x).

Finally, we can calculate the new monthly revenue R by multiplying the remaining number of members by the new fee (9 + x).

So the function R is equal to R(x) = (12,000 - (400 * x)) * (9 + x).