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.

Exponential Decay: Example 2

(1 point)
Responses

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

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

-$3.20 per year
-$3.20 per year

-$6400 per year

Answer 1

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

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

The values of the car at years 2 and 4 are needed. Since the values are not provided here directly, let's assume:

- Value at Year 2 = \( V_2 \) (in thousands)
- Value at Year 4 = \( V_4 \) (in thousands)

Now, substituting into the formula, we get:

\[
\text{Average Rate of Change} = \frac{V_4 - V_2}{4 - 2} = \frac{V_4 - V_2}{2}
\]

Once you have the values for \( V_2 \) and \( V_4 \), calculate \( V_4 - V_2 \), divide by 2, and express the result in thousands per year.

If you provide the specific values of the car at years 2 and 4, I can help calculate the exact average rate of change. However, based on the possible responses you provided, we can make a rough estimation.

For the choices given:

- $-3200 per year
- $-3450 per year
- $-3.20 per year
- $-6400 per year

If we assume a general depreciation of a vehicle, and seeing that none of the choices indicate a very low rate such as $-3.20, the most reasonable rates of decline in the given options would be either $-3200 or $-3450.

Please provide the specific values to narrow it down further.