Question

find and interpret the average rate of change illustrated in the following graph.
find the average rate of change. select the correct choice below and fill in the answer box to complete your choice.
(type a whole number.)
a. the average rate of change is -$ 4000 per year.
b. the average rate of change is $ per year.
interpret the average rate of change. select the correct choice below and fill in the answer box to complete your choice.
(type a whole number.)
a. the value of the machine is decreasing $ each year during these years.
b. the value of the machine is increasing $ each year during these years.
c. the value of the machine is constant.

Explanation:

Step1: Calculate the average rate of change

The formula for the average rate of change is $\frac{y_2 - y_1}{x_2 - x_1}$.
Let $(x_1,y_1)=(0,16)$ and $(x_2,y_2)=(4,0)$.
$\frac{0 - 16}{4 - 0}=\frac{-16}{4}=-4$.
Since $y$ is in thousands of dollars, the average rate of change is $- 4000$ dollars per year.

Step2: Interpret the average rate of change

The negative sign in the average rate of change $-4000$ indicates that the value is decreasing.

Answer:

A. The average rate of change is $-\$4000$ per year.
A. The value of the machine is decreasing $\$4000$ each year during these years.