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.
Numbers of Hours Worked | 0 | 5 | 15 | 25 | 35 | 40 |
Total Earnings | $20.00 | $65.75 | $151.35 | $238.75 | $326.25 | $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 find the slope of the linear relationship between the number of hours worked and the total earnings.
Let's pick two points from the table to calculate the slope. Let's use the points (0, $20.00) and (40, $370.00).
Slope = (change in total earnings) / (change in number of hours worked)
= ($370.00 - $20.00) / (40 - 0)
= $350.00 / 40
= $8.75
Therefore, the rate of change of the contractor's total earnings with respect to the number of hours worked is $8.75 per hour.