Given the function that determines the bill:
[tex]b(x)=\begin{cases}0.15x\text{ , }x\leq200^{} \\ \\ 0.10(x-200)+30,\text{ }x>200\end{cases}\text{ }[/tex]
You know that "x" represents the number of kilowatt-hours (kWh) used in a month
Since you have to find the bill for a person who uses 400 kWh in a month, you can need to use the second equation, because the value of "x" is, in this case:
[tex]x=400[/tex]
And:
[tex]400>200[/tex]
Therefore, substituting that value of "x" into the second equation and evaluating, you get:
[tex]\begin{gathered} b(x)=0.10(x-200)+30 \\ \\ b(400)=0.10(400-200)+30 \end{gathered}[/tex]
[tex]\begin{gathered} b(400)=0.10(200)+30 \\ \\ b(400)=20+30 \\ \\ b(400)=50 \end{gathered}[/tex]
Hence, the answer is: Option A.
