Question

Fred repairs and sells used cars. He made this table to show the approximate value of a mid-size car over time.

Age(years)|Value
3|16500
4|14400
5|12700
6|11100
7|9500

Complete the sentence to describe the average rate of change shown in the table.

The car's value decreases by about ___ per year.

Answer 1

To find the average rate of change in the car's value per year, we can calculate the change in value over the change in age for the entire duration represented in the table.

The value of the car decreases from $16,500 (at age 3 years) to $9,500 (at age 7 years).

The change in value is:
\[
\text{Change in value} = 9500 - 16500 = -7000
\]

The change in age is:
\[
\text{Change in age} = 7 - 3 = 4
\]

Now, we can calculate the average rate of change:

\[
\text{Average rate of change} = \frac{\text{Change in value}}{\text{Change in age}} = \frac{-7000}{4} = -1750
\]

This means the car's value decreases by about $1,750 per year.

Thus, the completed sentence is:

The car's value decreases by about **$1,750** per year.