11. Sydney bought a new car for $32,000.00

Question

.

If the car depreciates in a 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.

x f(x)
0 32,000
1 29,440
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 using the given model $f(x)=32,000(0.92{)}^x$, we can substitute $x=3$ into the equation.

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

Now, first we need to calculate $(0.92{)}^3$:

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

Now multiply this result by 32,000:

$$f(3)=32,000\times 0.778688\approx 24,973.96608$$

Rounding this to the nearest cent gives:

$$f(3)\approx 24,973.97$$

Therefore, the value of the car after three years is $\text{Math not terminated in text box}$.