Function Word Problem

Question

The telephone company charges a fee of $6.50 per month for the first 100 message units and an additional fee of $0.06 for each of the next 100 message units. A reduced rate of $0.05 is charged for each message unit after the first 200 units. Express the monthly charge C as a function of the number of message units u.

Answer 1

Hi Daemyn.

 

This is going to be a Piecewise function with three different functions, depending on what "x" is:

 

C(x) = 6.50            1 ≤ x ≤ 100

 

C(x) = 6.50 + 0.06*x          101 ≤ x ≤ 200

 

C(x) = 6.50 + 6.00 + 0.05*x          x≥201

 

That's it. The 6.00 in the third equation shows up because the second 100 units costs 6.00 dollars (0.06 per message). I just kept the 6.50 and 6.00 separate, in order for you to see where each value comes from. you can combine them to 12.50, if you like...but I think it's clearer this way.

 

Best wishes.

 

Raffi