In April 2009, Nicor Gas had the following rate schedule for natural gas usage in singlefamily residences:

Monthly customer charge             $8.40
Distribution charge
1st 20 therms                  $0.1473/therm
Next 30 therms               $0.0579/therm
Over 50 therms               $0.0519/therm
Gas supply charge               $0.43/therm

(a) What is the charge for using 40 therms in a month?

(b) What is the charge for using 150 therms in a month?

(c) Develop a model that gives the monthly charge C for x therms of gas.

(d) Graph the function found in part (c).