Questions: The following graph shows the decreasing value of a car over time. (See Example 5 in this section.) (a) Write a sentence that explains the meaning of the ordered pair (4,8700). After years the car has a value of (b) Find the average rate of change (in dollars per year) of car value for the given points. per year

The following graph shows the decreasing value of a car over time. (See Example 5 in this section.)
(a) Write a sentence that explains the meaning of the ordered pair (4,8700).

After years the car has a value of

(b) Find the average rate of change (in dollars per year) of car value for the given points.
per year

Transcript text: The following graph shows the decreasing value of a car over time. (See Example 5 in this section.) (a) Write a sentence that explains the meaning of the ordered pair $(4,8700)$. After $\square$ years the car has a value of $\$$ $\square$ (b) Find the average rate of change (in dollars per year) of car value for the given points. \$ $\square$ per year

Solution

Solution Steps

Step 1: Interpret the ordered pair (4, 8700)

The ordered pair (4, 8700) represents a point on the graph where the x-coordinate (4) corresponds to the time in years and the y-coordinate (8700) corresponds to the car's value in dollars. This means that after 4 years, the car's value is $8700.

After $ \boxed{4} $ years the car has a value of $ \$ \boxed{8700} $.

Step 2: Calculate the change in car value

We are given two points on the graph: (2, 16150) and (4, 8700). The change in car value is the difference between the y-coordinates: 8700 - 16150 = -7450.

Step 3: Calculate the change in time

The change in time is the difference between the x-coordinates: 4 - 2 = 2.

Step 4: Calculate the average rate of change

The average rate of change is the change in car value divided by the change in time: -7450 / 2 = -3725