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, you can use the formula \( f(x) = 32,000(0.92)^x \). In this case, \( x = 3 \).

Now, let's calculate \( f(3) \):

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

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

\[ (0.92)^3 \approx 0.778688 \]

Now, multiply this value by 32,000:

\[ f(3) = 32,000 \times 0.778688 \approx 24,988.00 \]

Thus, the value of the car after three years is approximately $24,988.00.

So, filling in the table:

\[ \text{The value of the car after three years is } $24,988.00. \]