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 function f(x)=32,000(0.92)x. Complete the table to find the value of the car to the nearest cent after three years.

Question

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

Answer 1

To find the value of the car after three years, we can substitute \( x = 3 \) into the function \( f(x) = 32,000(0.92)^x \).

So, we calculate:

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

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

\[ (0.92)^3 = 0.7738 \]

Now, multiply this value by 32,000:

\[ f(3) = 32,000 \times 0.7738 = 24,758.40 \]

Therefore, the value of the car after three years is $24,758.40.