Question

11. 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)

Answer 1

To find the value of the car after three years, we can use the given equation:

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

For \(x = 3\):

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

First, calculate \(0.92^3\):

\[
0.92^3 = 0.778688
\]

Now, substituting this value back into the equation:

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

Calculating that:

\[
f(3) = 32,000 \times 0.778688 = 24,000.00 + 24,000.00 \times 0.778688 = 24,000.00 + 18,000.00 + 12,000.00 + 8,000.00 + 4,000.00 = 24,992 + 262 = 24,992.00 + 262.04 = 24,992.00 + 2,962.00 = 24,992.00 + 2,962.00 = 24,992
\]

After performing the multiplication, we find the final value:

\[
f(3) = 24,991.00
\]

So, the value of the car after three years, rounded to the nearest cent, is:

\[
\text{The value of the car after three years is } \$24,991.00.
\]