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 $
1 answer
To calculate the value of the car after three years using the depreciation equation \( f(x) = 32,000(0.92)^x \):
Calculate \( f(3) \): \[ f(3) = 32,000(0.92)^3 \]
Calculate \( (0.92)^3 \): \[ (0.92)^3 = 0.778688 \]
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.
