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: Identify initial values
Initial number of members is 10400, initial monthly - fee is $8.
Step2: Determine new monthly - fee and number of members
The new monthly - fee is $(8 + x)$ dollars. The number of members after the price increase is $(10400-400x)$ (since 400 members leave for each $1 increase in the fee).
Step3: Calculate the revenue function
Revenue $R(x)$ is the product of the number of members and the monthly - fee. So $R(x)=(10400 - 400x)(8 + x)$. Expand the product: [ \begin{align*} R(x)&=10400\times8+10400x-400x\times8-400x^{2}\ &=83200 + 10400x-3200x-400x^{2}\ &=- 400x^{2}+7200x + 83200 \end{align*} ]
Answer:
$R(x)=-400x^{2}+7200x + 83200$