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. Find the value of the car to the cent after three years

Answer 1

To find the value of the car after three years, we can use the provided function:

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

We need to substitute \( x = 3 \) into the equation to find \( f(3) \):

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

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

\[ (0.92)^3 = 0.778688 \]

Now, we can multiply this value by $32,000:

\[ f(3) = 32,000 \times 0.778688 \]

Calculating the above:

\[ f(3) \approx 24,996.00 \]

Thus, the value of the car after three years is approximately $24,996.00 (to the cent).