Use the table to answer the question.

Question

x f(x)
0 32000
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.

(2 points)
The value of the car after three years is $

Answer 1

To find the value of the car after three years using the provided formula \( f(x) = 32,000(0.92)^x \), we need to substitute \( x = 3 \) into the equation.

Calculating \( f(3) \):

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

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

\[ (0.92)^3 = 0.778688 \]

Now, multiply this by \( 32,000 \):

\[ f(3) = 32,000 \times 0.778688 \approx 24,988.00 \]

So, the value of the car after three years is approximately:

\[ f(3) \approx 24,988.00 \]

Thus, the value of the car after three years is $24,988.00.