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 $736.
He will make $736.

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

He will make $644.
He will make $644.
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Answer 1

To calculate how much Garrett will make for the week, we will use the piecewise function given:

• For hours worked \( x \) where \( 0 \leq x \leq 8 \), his pay is \( f(x) = 14x \).
• For hours worked \( x \) where \( 8 < x \leq 24 \), his pay is \( f(x) = 16x - 16 \).

Now, let's calculate his earnings for each day of the week based on the hours he worked:

1. Monday (12 hours):
   Since \( 12 > 8 \), we use the second part of the function:
   \[ f(12) = 16(12) - 16 = 192 - 16 = 176 \]

2. Tuesday (8 hours):
   Since \( 8 \leq 8 \), we use the first part of the function:
   \[ f(8) = 14(8) = 112 \]

3. Wednesday (8 hours):
   Since \( 8 \leq 8 \), we use the first part of the function:
   \[ f(8) = 14(8) = 112 \]

4. Thursday (8 hours):
   Since \( 8 \leq 8 \), we use the first part of the function:
   \[ f(8) = 14(8) = 112 \]

5. Friday (10 hours):
   Since \( 10 > 8 \), we use the second part of the function:
   \[ f(10) = 16(10) - 16 = 160 - 16 = 144 \]

Now, let's sum the earnings from each day:

• Monday: $176
• Tuesday: $112
• Wednesday: $112
• Thursday: $112
• Friday: $144

Now adding them up:

\[ 176 + 112 + 112 + 112 + 144 = 656 \]

Thus, Garrett will make $656 for the week.

So the correct response is:

He will make $656.