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 depreciation model \( f(x) = 32,000(0.92)^x \), we can substitute \( x = 3 \):

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

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

\[ 0.92^3 = 0.7792 \quad (\text{approximately}) \]

Now, multiply this value by 32,000:

\[ f(3) = 32,000 \times 0.7792 \]

Calculating that gives us:

\[ f(3) = 32,000 \times 0.7792 = 24,942.40 \]

Thus, the value of the car after three years is approximately $24,942.40.