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 of depreciation, we can use the equation given, \( f(x) = 32,000(0.92)^x \).

For \( x = 3 \):

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

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

\[ (0.92)^3 = 0.77378 \]

Now, multiply this by 32,000:

\[ f(3) = 32,000 \times 0.77378 \approx 24,790.96 \]

Thus, the value of the car after three years is approximately $24,790.96.

The completed table is:

\[ \begin{array}{|c|c|} \hline x & f(x) \ \hline 0 & 32,000.00 \ 1 & 29,440.00 \ 2 & 27,048.80 \ 3 & 24,790.96 \ \hline \end{array} \]