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]
