A contractor's total earnings from a job include a fixed amount plus an amount based on the number of hours worked. The values in the table represent the linear relationship between the number of hours worked and the contractor's total earnings in dollars.
Number of Hours Worked
Total Earnings
0
$20.00
5
$63.75
15
$151.25
25
$238.75
35
$326.25
40
$370.00
What is the rate of change of the contractor's total earnings in dollars with respect to the number of hours worked?
To find the rate of change, we need to determine the amount earned per hour worked.
First, let's find the fixed amount that the contractor earns regardless of the number of hours worked. This can be found by determining the y-intercept of the linear relationship.
Using the points (0, $20.00) and (5, $63.75), we can calculate the slope:
Slope = (63.75 - 20) / (5 - 0) = $43.75 / 5 hours = $8.75 per hour
Now that we have the fixed amount ($20) and the amount earned per hour ($8.75), we can express the total earnings (T) as a function of the number of hours worked (H):
T = $20 + $8.75H
The rate of change of the contractor's total earnings with respect to the number of hours worked is the coefficient of H, which is $8.75 per hour. This means that for every additional hour worked, the contractor earns an additional $8.75.