Question

Use the table to answer the question.

Monday 12 hours
Tuesday 8 hours
Wednesday 8 hours
Thursday 8 hours
Friday 10 hours
Garrett works at the pizza shop. He gets paid $14.00 per hour if he works 8 hours or less in a day. If Garrett works more than 8 hours in a day, he receives an extra $2.00 for every hour he works over 8 hours. For example, if Garrett works 10 hours, he receives $14.00 per hour for the first 8 hours and $16.00 per hour for the last 2 hours. The piecewise function represents the amount of money Garrett will make each day if he works x hours for the day. The table provides the hours Garrett worked each day for the week. Use the table and piecewise function to determine how much he will make for the week.

f(x)={14x,16x−16, 0≤x≤88<x≤24


(1 point)
Responses

He will make $656.
He will make $656.

He will make $736.
He will make $736.

He will make $644.
He will make $644.

He will make $46.
He will make $46.
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Answer 1

To calculate how much Garrett will make for the week based on the hours he worked each day and the piecewise function, we'll evaluate his earnings for each day using the provided function:

- **Monday (12 hours)**:
- For the first 8 hours: \( 8 \text{ hours} \times \$14.00/\text{hour} = \$112.00 \)
- For the additional 4 hours: \( 4 \text{ hours} \times \$16.00/\text{hour} = \$64.00 \)
- Total for Monday: \( \$112.00 + \$64.00 = \$176.00 \)

- **Tuesday (8 hours)**:
- Total for Tuesday: \( 8 \text{ hours} \times \$14.00/\text{hour} = \$112.00 \)

- **Wednesday (8 hours)**:
- Total for Wednesday: \( 8 \text{ hours} \times \$14.00/\text{hour} = \$112.00 \)

- **Thursday (8 hours)**:
- Total for Thursday: \( 8 \text{ hours} \times \$14.00/\text{hour} = \$112.00 \)

- **Friday (10 hours)**:
- For the first 8 hours: \( 8 \text{ hours} \times \$14.00/\text{hour} = \$112.00 \)
- For the additional 2 hours: \( 2 \text{ hours} \times \$16.00/\text{hour} = \$32.00 \)
- Total for Friday: \( \$112.00 + \$32.00 = \$144.00 \)

Now, we add up the totals for each day:

\[
\text{Total Earnings} = \$176.00 + \$112.00 + \$112.00 + \$112.00 + \$144.00
\]
\[
\text{Total Earnings} = \$176.00 + 3 \times \$112.00 + \$144.00
\]
\[
\text{Total Earnings} = \$176.00 + \$336.00 + \$144.00
\]
\[
\text{Total Earnings} = \$176.00 + \$480.00
\]
\[
\text{Total Earnings} = \$656.00
\]

Therefore, the total amount Garrett will make for the week is **$656**.