To find the monthly bill for a person who uses 600 kWh, we'll use the piecewise function given:
[tex]\[ b(x)=\begin{cases} 0.10 x & \text{if } x \leq 200 \\ 0.15(x-200) + 20 & \text{if } x > 200 \end{cases} \][/tex]
First, we need to determine which part of the piecewise function to use. Since the person used 600 kWh, we see that [tex]\( 600 > 200 \)[/tex]. Hence, we will use the second part of the piecewise function:
[tex]\[ b(x) = 0.15(x-200) + 20 \][/tex]
Now, substitute [tex]\( x = 600 \)[/tex] into the function:
[tex]\[ b(600) = 0.15(600 - 200) + 20 \][/tex]
Simplify inside the parentheses:
[tex]\[ b(600) = 0.15(400) + 20 \][/tex]
Next, calculate [tex]\( 0.15 \times 400 \)[/tex]:
[tex]\[ 0.15 \times 400 = 60 \][/tex]
Now add 20 to the result:
[tex]\[ b(600) = 60 + 20 = 80 \][/tex]
Therefore, the bill for a person who uses 600 kWh in a month is [tex]\(\$ 80\)[/tex].
So, the correct answer is:
A. \$ 80
