Pricing for natural gas: A local gas company charges $0.75 per therm for natural gas, up to 25 therms. Once the 25 therms has been exceeded, the charge doubles to $1.50 per therm due to limited supply and great demand. (a) Write these charges for natural gas consumption in the form of a piecewise-defined function C(t), where C(t) is the charge for t therms. Include the domain for each piece. Then (b) sketch the graph and determine the cost to a household that used 45 therms during a very cold winter month.
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