Question

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.
Hours, h 5 10 15 20 30 40

Pay, c(h) , in $ 97.50 195.00 292.50 390.00 585.00 780.00

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?
A. Sara should choose to work remotely since she can earn an extra $10.00 per week under that pay model.
B. Sara should choose to work remotely since she can earn an extra $60.00 per week under that pay model.
C. Sara should choose to work in person since she can earn $720.00 per week.
D. Sara should choose to work in person since she can earn $770.00 per week.

Answer 1

First, we need to calculate Sara's pay for both in-person and remote work situations if she works exactly 40 hours per week.

**In-person Compensation Plan:**

Using the function \( c(h) = 50 + 18h \):

1. Substitute \( h = 40 \):
\[
c(40) = 50 + 18 \times 40
\]
\[
c(40) = 50 + 720
\]
\[
c(40) = 770
\]

So, if Sara works in person for 40 hours, she will earn **$770.00**.

**Remote Compensation Plan:**

From the provided table, we see that for **40 hours**, the pay is **$780.00**.

Now, let's compare the two earnings:

- In-person pay: **$770.00**
- Remote pay: **$780.00**

Sara's pay is higher when she works remotely by:
\[
780 - 770 = 10.00
\]

Thus, the answer is:

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