Question

Use the table to answer the 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 $

Answer 1

To find the value of the car after three years, we can use the provided equation for depreciation:

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

where \( x \) is the number of years since the purchase.

For \( x = 3 \):

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

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

\[ (0.92)^3 = 0.778688 \]

Now, substituting this value back into the equation:

\[ f(3) = 32,000 \times 0.778688 \] \[ f(3) \approx 24,996.00 \]

Thus, rounding to the nearest cent, the value of the car after three years is approximately:

\[ \text{The value of the car after three years is } $24,996.00. \]