Question
Jack works after school. Each day he earns a set amount, plus an hourly wage.
Hours 1 1.5 2 2.5 3
Pay 18 23 28 33 38
Part A
Write a linear function f Jack can use to determine his pay.
A. f(x) = 10x + 8
B. f(x) = 15x + 3
C. f(x) = 0.5x + 1
D. f(x) = x + 18
Part B
Which is a reasonable domain?
A. 0 < x < 6
B. 0 < x < 24
C. 0 < x < 68
D. 0 < x < 248
Part C
Assume Jack works from 2:30 P.M. to 7:00 P.M. How much would he earn?
A. $33
B. $35.50
C. $45
D. $53
Hours 1 1.5 2 2.5 3
Pay 18 23 28 33 38
Part A
Write a linear function f Jack can use to determine his pay.
A. f(x) = 10x + 8
B. f(x) = 15x + 3
C. f(x) = 0.5x + 1
D. f(x) = x + 18
Part B
Which is a reasonable domain?
A. 0 < x < 6
B. 0 < x < 24
C. 0 < x < 68
D. 0 < x < 248
Part C
Assume Jack works from 2:30 P.M. to 7:00 P.M. How much would he earn?
A. $33
B. $35.50
C. $45
D. $53
Answers
GPT-4o mini
To solve this problem step by step for each part:
### Part A: Write a Linear Function
To determine his pay, we can analyze the provided data:
Hours: 1, 1.5, 2, 2.5, 3
Pay: $18, $23, $28, $33, $38
From the information:
1. When he works 1 hour, he earns $18.
2. When he works 3 hours, he earns $38.
This indicates that there is a base pay plus an hourly wage.
First, we can determine the hourly wage and the base pay:
From hour increments:
- From hour 1 to 1.5: $23 - $18 = $5 for 0.5 hours → hourly wage = $5 / 0.5 = $10/hour.
Checking at another point:
- From hour 2 to 2.5: $33 - $28 = $5 for 0.5 hours → hourly wage = $10/hour.
Determining base pay:
From the first hour:
- Pay for 1 hour = base pay (B) + hourly wage (10)
18 = B + 10
B = 18 - 10 = $8.
Thus, the linear function:
\[ f(x) = 10x + 8 \]
The correct answer is: **A. f(x) = 10x + 8**
### Part B: Reasonable Domain
For Jack's working hours, the reasonable domain is typically constrained by the maximum hours one could work in a day.
- The options suggest hours that range from less than 6 hours up to 248 hours, but practically, a high school student like Jack wouldn't work close to 24 hours in a day.
Given these considerations:
- Option A assumes: 0 < x < 6 (This means he can work up to 5 hours and is reasonable for afternoon shifts.)
- Other options (B, C, D) involve hours that are unrealistic or impractical for after-school work.
Thus, the reasonable domain is: **A. 0 < x < 6**
### Part C: How Much Would He Earn?
If Jack works from 2:30 P.M. to 7:00 P.M.:
- **Total time worked = 4.5 hours**
- Using the function derived:
\[ f(4.5) = 10(4.5) + 8 = 45 + 8 = 53 \]
So, Jack would earn: **D. $53**
### Summary of Answers:
- Part A: A. f(x) = 10x + 8
- Part B: A. 0 < x < 6
- Part C: D. $53
### Part A: Write a Linear Function
To determine his pay, we can analyze the provided data:
Hours: 1, 1.5, 2, 2.5, 3
Pay: $18, $23, $28, $33, $38
From the information:
1. When he works 1 hour, he earns $18.
2. When he works 3 hours, he earns $38.
This indicates that there is a base pay plus an hourly wage.
First, we can determine the hourly wage and the base pay:
From hour increments:
- From hour 1 to 1.5: $23 - $18 = $5 for 0.5 hours → hourly wage = $5 / 0.5 = $10/hour.
Checking at another point:
- From hour 2 to 2.5: $33 - $28 = $5 for 0.5 hours → hourly wage = $10/hour.
Determining base pay:
From the first hour:
- Pay for 1 hour = base pay (B) + hourly wage (10)
18 = B + 10
B = 18 - 10 = $8.
Thus, the linear function:
\[ f(x) = 10x + 8 \]
The correct answer is: **A. f(x) = 10x + 8**
### Part B: Reasonable Domain
For Jack's working hours, the reasonable domain is typically constrained by the maximum hours one could work in a day.
- The options suggest hours that range from less than 6 hours up to 248 hours, but practically, a high school student like Jack wouldn't work close to 24 hours in a day.
Given these considerations:
- Option A assumes: 0 < x < 6 (This means he can work up to 5 hours and is reasonable for afternoon shifts.)
- Other options (B, C, D) involve hours that are unrealistic or impractical for after-school work.
Thus, the reasonable domain is: **A. 0 < x < 6**
### Part C: How Much Would He Earn?
If Jack works from 2:30 P.M. to 7:00 P.M.:
- **Total time worked = 4.5 hours**
- Using the function derived:
\[ f(4.5) = 10(4.5) + 8 = 45 + 8 = 53 \]
So, Jack would earn: **D. $53**
### Summary of Answers:
- Part A: A. f(x) = 10x + 8
- Part B: A. 0 < x < 6
- Part C: D. $53