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 calculate the value of the car after three years using the depreciation equation $f(x)=32,000(0.92{)}^x$:

1. Calculate $f(3)$: $$f(3)=32,000(0.92{)}^3$$

2. Calculate $(0.92{)}^3$: $$(0.92{)}^3=0.778688$$

3. Now calculate $f(3)$: $$f(3)=32,000\times 0.778688\approx 24,964.00$$

Thus, rounding to the nearest cent, the value of the car after three years is $24,964.00.