The rate of change in Sam's work hours is 8 hours per week, as hours increased by 8 each week from 20 to 28 to 36. The initial value, representing the first week's work hours without orientation, is estimated at 12 hours. The rate of change reflects consistent weekly increases in hours worked, while the initial value indicates a start point for these calculations.
The question asks us to find and interpret the rate of change and the initial value of Sam's work hours, assuming a linear relationship between the weeks and the hours worked. The hours for the 2nd, 3rd, and 4th weeks were 20, 28, and 36 hours respectively.
To find the rate of change, we calculate the increase in hours per week. Between the 2nd and 3rd weeks, the increase is 8 hours, and between the 3rd and 4th weeks, it is also 8 hours. This indicates that the rate of change is 8 hours per week. The initial value is the number of hours Sam would have worked in the first week had it not included the orientation.
To find the initial value, we can work backward from the 2nd week. Since the rate of change is 8 hours, we subtract 8 hours from the 2nd week's hours (20 hours) to estimate the first week's hours, which would be 12 hours. Thus, the initial value representing Sam's work hours without orientation is 12 hours.
As for interpretation, the rate of change means Sam is working 8 more hours each subsequent week, and the initial value suggests that she started off working 12 hours in her first week, excluding orientation time.