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:
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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: \( $112.00 + $64.00 = $176.00 \)
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Tuesday (8 hours):
- Total for Tuesday: \( 8 \text{ hours} \times $14.00/\text{hour} = $112.00 \)
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Wednesday (8 hours):
- Total for Wednesday: \( 8 \text{ hours} \times $14.00/\text{hour} = $112.00 \)
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Thursday (8 hours):
- Total for Thursday: \( 8 \text{ hours} \times $14.00/\text{hour} = $112.00 \)
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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.
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