Use the table to answer the question.

Question

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 using the given depreciation model \( f(x) = 32,000(0.92)^x \), we can substitute \( x = 3 \) into the equation.

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

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

\[ (0.92)^3 = 0.92 \times 0.92 \times 0.92 \approx 0.778688 \]

Now, substitute this value back into the equation:

\[ f(3) = 32,000 \times 0.778688 \approx 24,979.00 \]

So the value of the car after three years is approximately $24,979.00.

Thus, the completed sentence is: The value of the car after three years is $24,979.00.