Question

Use the table to answer the 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.

(2 points)
The value of the car after three years is $
.

Answer 1

To find the value of the car after three years, we can use the formula provided:

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

We need to calculate \( f(3) \):

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

First, calculate \( 0.92^3 \):

\[
0.92^3 = 0.778688
\]

Now, substitute this value back into the equation:

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

Calculating this:

\[
f(3) = 32,000 \times 0.778688 \approx 24,973.96
\]

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

\[
\text{The value of the car after three years is } \$24,973.96.
\]

Final answer:

**$24,973.96**