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