an online shopping club has 11,200 members when it charges $9 per month for membership. for each $1 monthly…
an online shopping club has 11,200 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
Explanation:
Step1: Determine the number of members
The initial number of members is 11200 and for each $1 increase ($x$ increases), the club loses 400 members. So the number of members is $11200 - 400x$.
Step2: Determine the monthly fee
The initial monthly fee is $9 and with $x$ $1 - dollar$ increases, the monthly fee is $9 + x$.
Step3: Find the revenue function
Revenue $R$ is the product of the number of members and the monthly fee. So $R(x)=(11200 - 400x)(9 + x)$. Expand the function: [ \begin{align*} R(x)&=11200\times9+11200x-400x\times9 - 400x^{2}\ &=100800+11200x - 3600x-400x^{2}\ &=- 400x^{2}+7600x + 100800 \end{align*} ]
Answer:
$R(x)=-400x^{2}+7600x + 100800$