Write a piece-wise function to represent this situation

Question

monthly service charge-$22.00

first 30 hours of usage -$0.00

next 50 hours of usage-$0.25/hour

over 80 hours of usage-$1.00/hour

 

Answer 1

So you have three conditions.

 

So let f(x) = {   22, for x<=30   

                   {   22 + .25(x-30), for 30<x<=80

                   {   22+ .25*(80-30) + 1.00(x-80), for x>80

 

Let's test if this works.

 

For 20 hours, evaluate f(20) = 22 which is the first part of the function.

For 70 hours, evaluate f(70) = 22+.25(70-30) = 22+10 = 32. Note that the only hours charged for is the amount over 30. If you used 70 hours, the first 30 are in the fixed price and only 70-30 = 40 is the number of hours at the additional charge.

 

For 100 hours, evaluate f(100)= 22 + .25(50) + 1(100-80) = 22+12.50 + 20 = 54.50. Note that all I did is take the middle part of the function and added the minutes after the 80 minutes. So if you used 100 minutes, only 20 of them are at the highest price.

 

Hope this helped.