Question

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Comparing & Creating Models Quick Check
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Question
Use the table to answer the question.

This table shows the relationship between number of hours worked, h, and the corresponding pay, c(h), in dollars.
Hours, h 5 10 15 20 30 40
Pay, c(h)
, in $ 97.50 195.00 292.50 390.00 585.00 780.00
Sara’s new employer offers two compensation plans. If Sara reports to work in person, her weekly pay per number of hours worked can be modeled by the function c(h)=50+18h
, where c(h)
is the amount of compensation in dollars, and h is the number of hours worked each week. If she chooses to work remotely, the table shows her pay per number of hours worked. Compare the two function models. If Sara wants to maximize her pay, which choice should she make and why, assuming she works exactly 40 hours per week?(1 point)
Responses

Sara should choose to work remotely since she can earn an extra $10.00 per week under that pay model.
Sara should choose to work remotely since she can earn an extra $10.00 per week under that pay model.

Sara should choose to work in person since she can earn $720.00 per week.
Sara should choose to work in person since she can earn $720.00 per week.

Sara should choose to work in person since she can earn $770.00 per week.
Sara should choose to work in person since she can earn $770.00 per week.

Sara should choose to work remotely since can earn an extra $60.00 per week under that pay model.
Sara should choose to work remotely since can earn an extra $60.00 per week under that pay model.
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Answer 1

To compare the two compensation models for Sara, we need to calculate her pay under both plans if she works exactly 40 hours a week.

1. **Remote Pay Model:** From the table for remote work, when Sara works 40 hours, her pay is:
\[
c(40) = 780 \text{ dollars}
\]

2. **In-Person Pay Model:** According to the function \(c(h) = 50 + 18h\), her pay when she works 40 hours is:
\[
c(40) = 50 + 18(40) = 50 + 720 = 770 \text{ dollars}
\]

Now we can compare both pay options:
- Remote Pay: **$780**
- In-Person Pay: **$770**

To determine which option Sara should choose to maximize her pay:
- Remote work pays more: **$780** vs. **$770**.

Therefore, Sara should choose to work remotely since she can earn **$60.00 more** per week under that pay model than with in-person work (780 - 720 = 60).

So the most accurate response would be:
**Sara should choose to work remotely since she can earn an extra $60.00 per week under that pay model.**