To determine the monthly bill using the given function [tex]\( b(x) \)[/tex], we need to follow the tiered billing rates described in the 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]
Given the usage of 600 kWh, we see that 600 kWh is more than 200 kWh, so we use the second part of the piecewise function:
[tex]\[ b(x) = 0.15(x - 200) + 20 \][/tex]
Substitute [tex]\( x = 600 \)[/tex] into the function:
[tex]\[ b(600) = 0.15(600 - 200) + 20 \][/tex]
First, we perform the subtraction inside the parentheses:
[tex]\[ 600 - 200 = 400 \][/tex]
Next, we multiply by 0.15:
[tex]\[ 0.15 \times 400 = 60 \][/tex]
Finally, we add 20 to the result:
[tex]\[ 60 + 20 = 80 \][/tex]
Therefore, the bill for a person who uses 600 kWh in a month is:
[tex]\[ \$ 80 \][/tex]
Hence, the correct answer is:
A. \$ 80
