Question

An online shopping club has 10,000 members when it charges $7 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.

Answer 1

The function that can be used in the online shopping club about its monthly revenue is:

`R = -400x^(2) +7200x+70000`

Explanation:

First, we're gonna take into account the different values we have in the exercise:

1. 10,000 members
2. $7 per month for membership
3. Loses of 400 members by each $1 monthly increase

How the variable
`x` represents the price increase, we can do the formula below:

• 
  `(10000 - 400x) * (7+x)`

In this formula, we represent in the first part that by each 1 in the variable
`x`, the total of members will be reduced in 400, in the second part, we mention that at the same time, the membership fee will be increased in the same value of
`x`. Now we must simplify this function:

• 
  `(10000 - 400x) * (7+x)`

We operate the values:

• 
  `70000+10000x-2800x-400x^(2)`

Solve we can:

• 
  `70000+7200x-400x^(2)`

And organize:

• 
  `-400x^(2) +7200x+70000`

At the end, how
`R` represents the monthly revenue received by the club, we use that variable for our formula:

• 
  `R=-400x^(2) +7200x+70000`