Answered

An electric company calculates a person's monthly bill from the number of kilowatt-hours (kWh), [tex]x[/tex], used.

The function [tex]b(x) = \left\{ \begin{array}{cl}
0.10 x, & x \leq 200 \\
0.15(x - 200) + 20, & x \ \textgreater \ 200
\end{array} \right.[/tex] determines the bill.

How much is the bill for a person who uses [tex]800 \text{kWh}[/tex] in a month?

A. [tex]\$80[/tex]
B. [tex]\$60[/tex]



Answer :

GinnyAnswer
Certainly! Let's calculate the bill for someone who uses 800 kWh in a month according to the given piecewise function \( b(x) \).

The given function to determine the bill is:
[tex]\[ b(x) = \begin{cases} 0.10x & \text{if } x \leq 200, \\ 0.15(x - 200) + 20 & \text{if } x > 200 \end{cases} \][/tex]

Here, \( x = 800 \) kWh. Since 800 kWh is greater than 200 kWh, we use the second part of the piecewise function:
[tex]\[ b(x) = 0.15(x - 200) + 20 \][/tex]

1. Substitute \( x = 800 \) into the formula:
[tex]\[ b(800) = 0.15(800 - 200) + 20 \][/tex]

2. Calculate the value inside the parentheses:
[tex]\[ b(800) = 0.15(600) + 20 \][/tex]

3. Multiply 0.15 by 600:
[tex]\[ b(800) = 90 + 20 \][/tex]

4. Add the two results together:
[tex]\[ b(800) = 110 \][/tex]

Therefore, the bill for a person who uses 800 kWh in a month is [tex]$\$[/tex] 110.00.

The answer is:
[tex]\[ \boxed{110.00} \][/tex]