Question

in march 2014, a gas company had the rate schedule shown to the right for natural gas usage in single-family residences.
(a) what is the charge for using 30 therms in a month?
(b) what is the charge for using 200 therms in a month?
(c) develop a function that models the monthly charge c for x therms of gas.
(d) graph the function found in part (c).

monthly service charge: $19.45
delivery charge
first 40 therms: $0.90744/therm
over 40 therms: $0
natural gas cost
first 40 therms: $0.3982/therm
over 40 therms: $0.5857/therm

Explanation:

Calculate charge for 30 therms

$$
LATEXBLOCK0
$$

Calculate charge for 200 therms

$$
LATEXBLOCK1
$$

Formulate the piecewise function

$$
LATEXBLOCK2
$$

Answer:

(a) The charge for using 30 therms is $58.62.

(b) The charge for using 200 therms is $165.39.

(c) The piecewise function modeling the monthly charge \(C(x)\) for \(x\) therms is:

$$ C(x) =
LATEXBLOCK0
$$

(d) The graph of the function consists of two linear segments:

• A steeper line starting at \((0, 19.45)\) and ending at \((40, 71.6736)\).
• A flatter line starting at \((40, 71.6736)\) and continuing to the right with a slope of \(0.5857\).