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 $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. Sara should choose to work in person since she can earn $720.00 per week.
Answers
GPT-4o mini
To determine which option provides Sara with a higher pay, we need to calculate her weekly pay based on both compensation models when she works exactly 40 hours.
1. **In-person pay calculation**:
The formula for her in-person pay is given by:
\[
c(h) = 50 + 18h
\]
Plugging in \( h = 40 \):
\[
c(40) = 50 + 18(40) = 50 + 720 = 770
\]
Thus, her pay for working in person for 40 hours is **$770.00**.
2. **Remote pay calculation**:
From the table provided, the pay for 40 hours worked is:
\[
780.00
\]
Now, we compare the two pay amounts:
- In-person pay: **$770.00**
- Remote pay: **$780.00**
Since Sara can earn **$780.00** by working remotely, which is **$10.00** more than the **$770.00** she would earn by working in person, the conclusion is that:
**Sara should choose to work remotely since she can earn an extra $10.00 per week under that pay model.**
1. **In-person pay calculation**:
The formula for her in-person pay is given by:
\[
c(h) = 50 + 18h
\]
Plugging in \( h = 40 \):
\[
c(40) = 50 + 18(40) = 50 + 720 = 770
\]
Thus, her pay for working in person for 40 hours is **$770.00**.
2. **Remote pay calculation**:
From the table provided, the pay for 40 hours worked is:
\[
780.00
\]
Now, we compare the two pay amounts:
- In-person pay: **$770.00**
- Remote pay: **$780.00**
Since Sara can earn **$780.00** by working remotely, which is **$10.00** more than the **$770.00** she would earn by working in person, the conclusion is that:
**Sara should choose to work remotely since she can earn an extra $10.00 per week under that pay model.**