Problem
A power company calculates a person's monthly bill from the number of kilowatt-hours (kWh), $x$, used. The function $b(x)=\left\{\begin{array}{ll}0.15 x, & x \leq 200 \\ 0.10(x-200)+30, & x>200\end{array}\right.$ determines the bill. How much is the bill for a person who uses $700 \mathrm{kWh}$ in a month?
Solution
Step 1 ：Given the function b(x) = \(\begin{cases} 0.15x, & x \leq 200 \\ 0.10(x-200)+30, & x>200 \end{cases}\), we need to find the value of b(700).
Step 2 ：Since 700 > 200, we use the second part of the function: \(0.10(700-200)+30\).
Step 3 ：Calculating the result: \(0.10(500)+30 = 50+30 = 80\).
Step 4 ：\(\boxed{80}\) is the bill for a person who uses 700 kWh in a month.
