miapadgeth
Answered

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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 [tex]\( 800 \)[/tex] kWh in a month?

A. [tex]\( \$ 80 \)[/tex]
B. [tex]\( \$ 110 \)[/tex]
C. [tex]\( \$ 60 \)[/tex]
D. [tex]\( \$ 90 \)[/tex]

Sagot :

GinnyAnswer
To determine the bill for a person who uses 800 kWh in a month, we need to follow the piecewise function given:

[tex]\[ b(x) = \begin{cases} 0.10x & \text{if } x \leq 200 \\ 0.15(x - 200) + 20 & \text{if } x > 200 \end{cases} \][/tex]

Here, the person used 800 kWh, which is greater than 200 kWh. Therefore, we will use the second part of the function:

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

We substitute [tex]\( x = 800 \)[/tex] into the function:

[tex]\[ b(800) = 0.15(800 - 200) + 20 \][/tex]

First, calculate the term within the parentheses:

[tex]\[ 800 - 200 = 600 \][/tex]

Next, multiply this result by 0.15:

[tex]\[ 0.15 \times 600 = 90 \][/tex]

Finally, add 20 to this result:

[tex]\[ 90 + 20 = 110 \][/tex]

Thus, the bill for a person who uses 800 kWh in a month is [tex]\(\$110\)[/tex].

The correct answer is:
[tex]\[ \boxed{110} \][/tex]
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