I have a friend asking me how to model this problem.
A club's annual due is 100 dollars per member, less 0.50 dollars for each member over 600 and plus 0.50 dollars for less than 600.
a. Find the mathematical model expressing the club's revenue f(x) as a function of the x number of members.
b. Prove that the function is continuous on its domain.
I would like to kindly ask the help of the members if my answers to my friend's question are correct. Thanks in advance.
For task (a), I modeled the revenue of the club using this function:
$f(x)$=$[100 + (600-x)(0.5)](x)$ for $0=<x=<800$
For task (b), based on my model, the function is continuous on its domain.
According to the conditions, we have:
If $\ x< 600\ $, $\ f(x)=(100+0.50)x $
If $\ x= 600\ $, $\ f(x)=(100)x $
If $\ x> 600\ $, $\ f(x)=(100-0.50)x $