Use the table to answer the question.

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.(1 point)
The value of the car after three years is $
.
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Answer 1

To find the value of the car after three years using the depreciation model $f(x)=32,000(0.92{)}^x$, we will substitute $x=3$ into the equation.

$$f(3)=32,000(0.92{)}^3$$

First, calculate $(0.92{)}^3$:

$$(0.92{)}^3=0.778688$$

Now, calculate the value of the car after three years:

$$f(3)=32,000\times 0.778688$$

$$f(3)\approx 24,995.00$$

Thus, the value of the car after three years is approximately $24,995.00.