Question

The table below shows the value of a car ($ in thousands) and the time (in years) since it was purchased. Find the average rate of change in value from years 1 to 3.



Time

(Years)

Car's Value

(Thousands)

0 30
1 28
2 25
3 22
4 20


Responses

-2,000 dollars per year
-2,000 dollars per year

-2,500 dollars per year
-2,500 dollars per year

-3,000 dollars per year
-3,000 dollars per year

-5,000 dollars per year

Answer 1

To find the average rate of change in value from years 1 to 3, we can use the formula for average rate of change:

\[
\text{Average Rate of Change} = \frac{\text{Value at time } t_2 - \text{Value at time } t_1}{t_2 - t_1}
\]

In this case, \(t_1 = 1\) and \(t_2 = 3\).

From the table, we have:
- Value at \(t_1 = 1\) year = 28 (thousands)
- Value at \(t_2 = 3\) years = 22 (thousands)

Now, plug in these values into the formula:

\[
\text{Average Rate of Change} = \frac{22 - 28}{3 - 1} = \frac{-6}{2} = -3
\]

This means the average rate of change is -3 (thousands dollars per year).

Since we are asked for the value in dollars, we convert it to dollars:

\(-3 \text{ thousand dollars per year} = -3,000 \text{ dollars per year}\).

So, the average rate of change in value from years 1 to 3 is:

**-3,000 dollars per year**