Question

Which one of the following statements correctly compares the rate of changes for the money earned, measured as dollars per delivery, between 2 and 4 deliveries and 6 and 8 deliveries?

a) The rate of change is the same in both intervals.
b) The rate of change is greater between 2 and 4 deliveries.
c) The rate of change is greater between 6 and 8 deliveries.
d) The rate of change cannot be determined from the given information.

Answer 1

The correct answer is (b) The rate of change is greater between 2 and 4 deliveries, since the same dollar increase represents a larger percentage increase when the base amount is smaller, which would be the case in the earlier interval.

Step-by-step explanation:

The student's question asks to compare the rate of changes for money earned, measured as dollars per delivery, between two intervals: between 2 and 4 deliveries, and between 6 and 8 deliveries. Based on the provided information, we understand that as the base amount increases, the same change (a $2 raise, for example) results in a decreasing growth rate. Therefore, if the money earned per delivery is increasing by a fixed amount, the growth rate would be higher in the earlier interval between 2 and 4 deliveries than in the later interval between 6 and 8 deliveries.

This is because the base amount (total earned before the additional deliveries) in the interval between 6 and 8 deliveries would be higher than that in the interval between 2 and 4 deliveries, resulting in a smaller percentage increase for the same absolute change in dollars. With these concepts in mind, the correct answer is (b) The rate of change is greater between 2 and 4 deliveries.