Question

1. (5 points) (1.25 points each) this graph is a model of the number of tenants in a particular apartment complex in its first 24 months. answer the questions below.

circle the correct answer to complete the following fill - in - the - blank questions:
a. from month 1 to month 11, the total population is (increasing / decreasing).
b. from month 1 to month 11, the average rate of change of the population is (greater / less) than the instantaneous rate of change in month 20.
c. the instantaneous rate of change in month 22 is (greater / less) than the average rate of change from month 1 to 24. 0.25cm
d. the instantaneous rate of change in month 4 is (greater / less) than the instantaneous rate of change in month 14.

Explanation:

Step1: Analyze population trend from 1 - 11 months

Observing the graph, as the months increase from 1 to 11, the number of tenants is going up. So the population is increasing.

Step2: Compare average and instantaneous rate from 1 - 11 months and month 20

The average rate of change from month 1 to 11 is the slope of the secant - line connecting the points at month 1 and month 11. The instantaneous rate of change at month 20 is the slope of the tangent - line at month 20. The secant - line from 1 to 11 has a steeper slope than the tangent - line at month 20. So the average rate of change from 1 to 11 is greater.

Step3: Compare instantaneous rate at month 22 and average rate from 1 - 24 months

The instantaneous rate of change at month 22 is the slope of the tangent - line at month 22. The average rate of change from month 1 to 24 is the slope of the secant - line connecting the points at month 1 and month 24. The tangent - line at month 22 has a smaller slope than the secant - line from 1 to 24. So the instantaneous rate at month 22 is less.

Step4: Compare instantaneous rates at month 4 and month 14

The instantaneous rate of change at month 4 is the slope of the tangent - line at month 4. The instantaneous rate of change at month 14 is the slope of the tangent - line at month 14. The tangent - line at month 4 has a smaller slope than the tangent - line at month 14. So the instantaneous rate at month 4 is less.

Answer:

A. increasing
B. greater
C. less
D. less