Chapter 2.3, Problem 94E

Natural-gas rates. Table 2 shows the rates for natural gas charged by the Middle Tennessee Natural Gas Utility District during winter months. The base charge is a fixed monthly charge, independent of the amount of gas used per month.

Table 2 Winter (October–April)

Base charge	$5.00
First 5 therms	0.69 per therm
Next 45 therms	0.65 per therm
Over 50 therms	0.63 per therm

1. (A)   Write a piecewise definition of the monthly charge S(x) for a customer who uses x therms in a winter month.
2. (B)   Graph S(x).
3. (C)   Is S(x) continuous at x = 5? At x = 50? Explain.