Question

Sydney bought a new car for $32,000.00
.

If the car depreciates in a value by 8%
each year, the situation can be modeled by the equationf(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 $32,000.00
1 $29,440.00
2 $27,048.80
3 ?
(1 point)
The value of the car after three years is $
(round your answer to the nearest cent)

Answers

GPT-4o mini
To find the value of the car after three years, we need to use the given formula \( f(x) = 32,000(0.92)^x \).

Substituting \( x = 3 \):

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

Calculating \( (0.92)^3 \):

\[
(0.92)^3 = 0.773789
\]

Now multiply by 32,000:

\[
f(3) = 32,000 \times 0.773789
\]

\[
f(3) = 24,777.24
\]

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

\[
\boxed{24,777.24}
\]

Rounded to the nearest cent, the answer is \( \$24,777.24 \).