Use the table to answer the question.

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 $46.
He will make $46.

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

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

He will make $736.

Answer 1

To calculate the amount Garrett will make for the week, we can break down his earnings for each day based on the hours he worked and the piecewise function provided.

The function given is:

• \( f(x) = 14x \) if \( 0 \leq x \leq 8 \)
• \( f(x) = 16x - 16 \) if \( 8 < x \leq 24 \)

Now let’s calculate the earnings for each day:

1. Monday (12 hours): Since he worked more than 8 hours: \[ f(12) = 16(12) - 16 = 192 - 16 = 176 \]

2. Tuesday (8 hours): Since he worked 8 hours: \[ f(8) = 14(8) = 112 \]

3. Wednesday (8 hours): Since he worked 8 hours: \[ f(8) = 14(8) = 112 \]

4. Thursday (8 hours): Since he worked 8 hours: \[ f(8) = 14(8) = 112 \]

5. Friday (10 hours): Since he worked more than 8 hours: \[ f(10) = 16(10) - 16 = 160 - 16 = 144 \]

Now summing up all the wages: \[ \text{Total earnings} = 176 + 112 + 112 + 112 + 144 = 656 \]

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

So the correct response is: He will make $656.