Use the table to answer the question.

Question

This table shows function values f(x) decreasing over time, with a missing value for x=3. x f(x)
0 32,000
1 29,440
2 27,048.80
3 ?
Sydney bought a new car for $32,000.00. If the car depreciates in value by 8% each year, the situation can be modeled by the equation f(x)=32,000(0.92)x
. Complete the table to find the value of the car to the nearest cent after three years.(1 point)
The value of the car after three years is $

Answer 1

To find the value of the car after three years, you can use the depreciation formula given in the question:

\[ f(x) = 32,000(0.92)^x \]

We need to calculate \( f(3) \):

\[ f(3) = 32,000(0.92)^3 \]

First, calculate \( (0.92)^3 \):

\[ (0.92)^3 = 0.778688 \]

Now, substitute this value back into the equation:

\[ f(3) = 32,000 \times 0.778688 \]

Now calculate \( 32,000 \times 0.778688 \):

\[ f(3) = 24,979.008 \]

To round to the nearest cent:

\[ f(3) \approx 24,979.01 \]

Thus, the value of the car after three years is approximately $24,979.01.