11. Sydney bought a new car for $32,000.00

Question

.

If the car depreciates in a 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.

x f(x)
0 32,000
1 29,440
2 27,048.80
3 ?
(1 point)
The value of the car after three years is $
(round your answer to the nearest cent)

Answer 1

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

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

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

\[ (0.92)^3 = 0.778688 \]

Now multiply this result by 32,000:

\[ f(3) = 32,000 \times 0.778688 \approx 24,973.96608 \]

Rounding this to the nearest cent gives:

\[ f(3) \approx 24,973.97 \]

Therefore, the value of the car after three years is \( \text{$} 24,973.97 \).