Use the table to answer the question. x f(x) 0: 32,000

Question

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 using the given equation \( f(x) = 32,000(0.92)^x \), we can plug in \( x = 3 \):

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

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

\[ 0.92^3 = 0.778688 \]

Now multiply this by $32,000:

\[ f(3) = 32,000 \times 0.778688 \approx 24,971.00 \]

Thus, the value of the car after three years is approximately:

\[ \text{Value of the car after three years} = $24,971.00 \]

So, the value of the car after three years is $24,971.00.