43. Cost of Natural Gas In April 2009, Peoples Energy had the following rate schedule for natural gas usage in single- family residences:

Monthly service charge $15.95 Per therm service charge

1st 50 therms $0.33606/therm

Over 50 therms $0.10580/therm

Gas charge $0.3940/therm

(a) What is the charge for using 50 therms in a month?

(b) What is the charge for using 500 therms in a month?

(c) Develop a model that relates the monthly charge C for

x therms of gas.

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

Source: Peoples Energy, Chicago, Illinois, 2009