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)

Answer 1

To find the value of the car after three years using the depreciation model \(f(x) = 32,000(0.92)^x\), we will substitute \(x = 3\) into the equation.

Calculating \(f(3)\):

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

Now we need to calculate \(0.92^3\):

\[ 0.92^3 = 0.778688 \]

Now substituting this value in:

\[ f(3) = 32,000 \times 0.778688 \] \[ f(3) \approx 24,956.00 \]

So, the value of the car after three years, rounded to the nearest cent, is approximately $24,956.00.

Updating the table:

| x | f(x) | |---|------------| | 0 | $32,000.00 | | 1 | $29,440.00 | | 2 | $27,048.80 | | 3 | $24,956.00 |