The rate of change of the contractor's total earnings with respect to the number of hours worked can be calculated by finding the difference in total earnings for consecutive hours worked and dividing by the difference in hours worked.
Using the data provided:
For hours worked = 0 to 5:
Rate of change = ($63.75 - $20.00) / (5 - 0) = $43.75 / 5 = $8.75 per hour
For hours worked = 5 to 15:
Rate of change = ($151.25 - $63.75) / (15 - 5) = $87.50 / 10 = $8.75 per hour
For hours worked = 15 to 25:
Rate of change = ($238.75 - $151.25) / (25 - 15) = $87.50 / 10 = $8.75 per hour
For hours worked = 25 to 35:
Rate of change = ($326.25 - $238.75) / (35 - 25) = $87.50 / 10 = $8.75 per hour
For hours worked = 35 to 40:
Rate of change = ($370.00 - $326.25) / (40 - 35) = $43.75 / 5 = $8.75 per hour
Therefore, the rate of change of the contractor's total earnings with respect to the number of hours worked is a constant $8.75 per hour.
What is the rate of change of the contractor's total earnings in dollars with respect to the number if hours worked?
number of Hours Worked: 0, 5, 15, 25, 35, 40
total earnings: $20.00, $63.75, $151.25, $238.75, $326.25, $370.00
1 answer