An electric company calculates a person's monthly bill from the number of kilowatt-hours (kWh), [tex]$x$[/tex], used.

The function [tex]b(x) = \left\{
\begin{array}{cl}
0.10x, & x \leq 200 \\
0.15(x-200) + 20, & x \ \textgreater \ 200
\end{array}
\right.[/tex] determines the bill.

How much is the bill for a person who uses 600 kWh in a month?

A. [tex]\$80[/tex]
B. [tex]\$60[/tex]
C. [tex]\[tex]$70[/tex]
D. [tex]\$[/tex]40[/tex]



Answer :

To determine the bill for a person who uses 600 kilowatt-hours (kWh) in a month, we need to evaluate the given 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]

Since the person has used 600 kWh, we are in the scenario where [tex]\( x > 200 \)[/tex]. So we will use the second piece of the function:

[tex]\[ b(x) = 0.15(x - 200) + 20 \][/tex]

Now, we substitute [tex]\( x = 600 \)[/tex] into the function:

[tex]\[ b(600) = 0.15(600 - 200) + 20 \][/tex]

Next, simplify inside the parentheses:

[tex]\[ 600 - 200 = 400 \][/tex]

So, the function becomes:

[tex]\[ b(600) = 0.15 \times 400 + 20 \][/tex]

Now, calculate [tex]\( 0.15 \times 400 \)[/tex]:

[tex]\[ 0.15 \times 400 = 60 \][/tex]

Add the 20:

[tex]\[ 60 + 20 = 80 \][/tex]

Thus, the bill for using 600 kWh in a month is:

[tex]\[ \$80 \][/tex]

So, the correct answer is:

A. \$80