Use the table to answer the question.

Question

x f(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
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)
The value of the car after three years is $.

Answer 1

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

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

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

\[ (0.92)^3 = 0.778688 \]

Now, substitute this back into the equation:

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

Now perform the multiplication:

\[ f(3) \approx 32,000 \times 0.778688 \approx 24,964.00 \]

Therefore, the value of the car after three years is approximately $24,964.00.