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 21.
d. the instantaneous rate of change in month 1 is (greater / less) than the instantaneous rate of change in month 11

Explanation:

Step1: Analyze population trend from 1 - 11 months

By 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 slope from 1 to 11 is steeper than the tangent - line slope 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 - 21 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 21 is the slope of the secant - line connecting the points at month 1 and month 21. The tangent - line slope at month 22 is less steep than the secant - line slope from 1 to 21. So the instantaneous rate of change at month 22 is less.

Step4: Compare instantaneous rates at month 1 and month 11

The instantaneous rate of change at month 1 is the slope of the tangent - line at month 1. The instantaneous rate of change at month 11 is the slope of the tangent - line at month 11. The tangent - line slope at month 1 is less steep than the tangent - line slope at month 11. So the instantaneous rate of change at month 1 is less.

Answer:

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