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) Car's value=(Thousands)
0 32
1 27.2
2 23.1
3 19.65
4 16.70

(1 point)
Responses

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

-$6,400 per year
-$6,400 per year

-$3.20 per year
-$3.20 per year

-$3,200 per year

Answer 1

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

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

Where:
- \( t_1 = 2 \) years, and the car's value at this time is \( 23.1 \) thousand dollars.
- \( t_2 = 4 \) years, and the car's value at this time is \( 16.70 \) thousand dollars.

Now we substitute the values into the formula:

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

Calculating the difference in value:

\[
16.70 - 23.1 = -6.4
\]

Calculating the difference in time:

\[
4 - 2 = 2
\]

Now, substituting these results back into the formula:

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

This means that the average rate of change in the car's value from years 2 to 4 is \(-3.2\) thousand dollars per year.

Thus, the answer is:

**-$3.20 per year**