Question

an electric company has the following rate schedule for electricity usage in single-family residences:

monthly service charge $4.93

per kilowatt service charge
1st 300 kilowatts $0.11589/kw
over 300 kilowatts $0.13321/kw

what is the charge for using 300 kilowatts in one month?
what is the charge for using 375 kilowatts in one month?
construct a function that gives the monthly charge c for x kilowatts of electricity.

Explanation:

Answer:

(a) \$4.93 + 300 \times 0.11589 = \$4.93 + \$34.767 = \$39.697 \approx \$39.70
(b) \$4.93 + 300 \times 0.11589 + (375 - 300) \times 0.13321 = \$39.697 + 75 \times 0.13321 = \$39.697 + \$9.99075 = \$49.68775 \approx \$49.69
(c) \( C(x) =

$$\begin{cases} 4.93 + 0.11589x & \text{if } 0 \leq x \leq 300 \\ 4.93 + 0.11589 \times 300 + 0.13321(x - 300) & \text{if } x > 300 \end{cases}$$

\)
Simplifying the second case: \( 4.93 + 34.767 + 0.13321x - 39.963 = 0.13321x - 0.266 \), so \( C(x) =

$$\begin{cases} 0.11589x + 4.93 & 0 \leq x \leq 300 \\ 0.13321x - 0.266 & x > 300 \end{cases}$$

\)