To determine the bill for a person who uses 600 kilowatt-hours (kWh) in a month, we need to evaluate the given piecewise function:
[tex]\[
b(x) =
\begin{cases}
0.10x & \text{if } x \leq 200 \\
0.15(x - 200) + 20 & \text{if } x > 200
\end{cases}
\][/tex]
Since the person has used 600 kWh, we are in the scenario where [tex]\( x > 200 \)[/tex]. So we will use the second piece of the function:
[tex]\[
b(x) = 0.15(x - 200) + 20
\][/tex]
Now, we substitute [tex]\( x = 600 \)[/tex] into the function:
[tex]\[
b(600) = 0.15(600 - 200) + 20
\][/tex]
Next, simplify inside the parentheses:
[tex]\[
600 - 200 = 400
\][/tex]
So, the function becomes:
[tex]\[
b(600) = 0.15 \times 400 + 20
\][/tex]
Now, calculate [tex]\( 0.15 \times 400 \)[/tex]:
[tex]\[
0.15 \times 400 = 60
\][/tex]
Add the 20:
[tex]\[
60 + 20 = 80
\][/tex]
Thus, the bill for using 600 kWh in a month is:
[tex]\[
\$80
\][/tex]
So, the correct answer is:
A. \$80
