an online shopping club has 10,400 members when it charges $8 per month for membership. for each $1 monthly…
an online shopping club has 10,400 members when it charges $8 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.\\nmonthly revenue = # members • monthly fee.
Answer
Explanation:
Step1: Determine the number of members after the change
The number of members decreases by 40 for each $1 increase in the fee. Initially, there are 10400 members. So the number of members after an $x$ - dollar increase in the fee is $10400 - 40x$.
Step2: Determine the monthly - fee after the change
The initial monthly fee is $8. After an $x$ - dollar increase, the new monthly fee is $8 + x$.
Step3: Calculate the revenue function
The monthly revenue $R(x)$ is the product of the number of members and the monthly fee. So $R(x)=(10400 - 40x)(8 + x)$. Expand the product using the FOIL method: [ \begin{align*} R(x)&=10400\times8+10400x-40x\times8 - 40x^{2}\ &=83200+10400x - 320x-40x^{2}\ &=- 40x^{2}+10080x + 83200 \end{align*} ]
Answer:
$R(x)=-40x^{2}+10080x + 83200$