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 2 to 4.
time (years) cars value (thousands)
0 32
1 27,2
2 23.1
3 19.65
4 16.70

(1 point)
Responses

-$3,200 per year
-$3,200 per year

-$3.20 per year
-$3.20 per year

-$3,450 per year
-$3,450 per year

-$6,400 per year

Answer 1

To find the average rate of change in the value of the car from years 2 to 4, we can use the formula for average rate of change, which is:

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

In this case, let \( t_1 = 2 \) years and \( t_2 = 4 \) years.

From the table:
- Value at \( t_1 = 2 \): \( 23.1 \) (thousands)
- Value at \( t_2 = 4 \): \( 16.70 \) (thousands)

Now, we can compute the average rate of change:

\[
\text{Average Rate of Change} = \frac{16.70 - 23.1}{4 - 2} = \frac{-6.4}{2} = -3.2
\]

This represents a rate of change of -3.2 (in thousands) per year. Since the answer is in thousands, we would express it as:

\[
-3.20 \text{ per year}
\]

Therefore, the correct response is:

**-$3.20 per year**