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.
y value
0 32
1 27.2
2 23.1
3 19.65
4 16.70

(1 point)
Responses

-$6400 per year
-$6400 per year

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

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

-$3.20 per year

Answer 1

To find the average rate of change in value from year 2 to year 4, we can use the formula:

\[
\text{Average Rate of Change} = \frac{\text{Value at year 4} - \text{Value at year 2}}{\text{Year 4} - \text{Year 2}}
\]

From the provided data:
- Value at year 4 = 16.70 (thousands)
- Value at year 2 = 23.1 (thousands)

Now substitute these values into the formula:

\[
\text{Average Rate of Change} = \frac{16.70 - 23.1}{4 - 2} = \frac{-6.4}{2} = -3.2 \text{ (thousands per year)}
\]

Since the values are in thousands of dollars, we express the average rate of change in dollars:

\[
-3.2 \, \text{thousands} = -3.2 \times 1000 = -3200 \, \text{dollars per year}
\]

Thus, the average rate of change in value from years 2 to 4 is:

**-$3,200 per year**