Answer:
The required equation :
[tex]y=(320-10x)(45+5x)=14400+1150x-50x^2[/tex]
Step-by-step explanation:
Given : A fitness center currently has 320 members. Monthly memberships fees are $45. The manager of the fitness center has determined that each time the membership increases by $5, approximately 10 members leave and go to a different gym.
To write : A equation that can be used to find the revenue of the fitness center in dollars,y, after x price increases of $5.
Solution :
Revenue is defined by the amount or price during specific period.
Let x be the number of months,
y be the revenue of the fitness center.
The number of members in the fitness center is 320 but after increasing $5 10 members leave.
So, the total member after increment in x months are [tex]320-10x[/tex]
Monthly memberships fees are $45.
The manager of the fitness center has determined that each time the membership increases by $5.
The price of monthly membership after increment is [tex]45+5x[/tex]
So, The equation which gave the revenue of the fitness center is
[tex]y=(320-10x)(45+5x)[/tex]
[tex]y=14400+1600x-450x-50x^2[/tex]
[tex]y=14400+1150x-50x^2[/tex]
