To determine the bill for a person who uses 800 kWh in a month, we need to follow the piecewise function given:
[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, the person used 800 kWh, which is greater than 200 kWh. Therefore, we will use the second part of the function:
[tex]\[ b(x) = 0.15(x - 200) + 20 \][/tex]
We substitute [tex]\( x = 800 \)[/tex] into the function:
[tex]\[ b(800) = 0.15(800 - 200) + 20 \][/tex]
First, calculate the term within the parentheses:
[tex]\[ 800 - 200 = 600 \][/tex]
Next, multiply this result by 0.15:
[tex]\[ 0.15 \times 600 = 90 \][/tex]
Finally, add 20 to this result:
[tex]\[ 90 + 20 = 110 \][/tex]
Thus, the bill for a person who uses 800 kWh in a month is [tex]\(\$110\)[/tex].
The correct answer is:
[tex]\[ \boxed{110} \][/tex]
