To determine the bill for a person who uses 400 kWh in a month, let's analyze the given piecewise function [tex]\( b(x) \)[/tex]:
[tex]\[ b(x)=
\begin{cases}
0.10x, & \text{if } x \leq 200 \\
0.15(x-200) + 20, & \text{if } x > 200
\end{cases}
\][/tex]
We are given [tex]\( x = 400 \)[/tex] kWh.
Since 400 kWh is greater than 200 kWh, we use the second part of the piecewise function:
[tex]\[ b(x) = 0.15(x - 200) + 20 \][/tex]
Now substitute [tex]\( x = 400 \)[/tex]:
[tex]\[ b(400) = 0.15(400 - 200) + 20 \][/tex]
Calculate the value inside the parentheses:
[tex]\[ 400 - 200 = 200 \][/tex]
Now multiply by 0.15:
[tex]\[ 0.15 \times 200 = 30 \][/tex]
Then add 20 to this result:
[tex]\[ 30 + 20 = 50 \][/tex]
Therefore, the bill for a person who uses 400 kWh in a month is \[tex]$50.
So the correct answer is:
C. \$[/tex]50
