Question
Sydney bought a new car for $32,000.00 . If the car depreciates in a value by 8% each year, the situation can be modeled by the equationf(x)=32,000(0.92)x Complete the table to find the value of the car to the nearest cent after three years.
x f(x)
0 $32,000.00
1. $29,440.00
2 $27,048.80
3 ?
(1 point) The value of the car after three years is $ (round your answer to the nearest cent)
x f(x)
0 $32,000.00
1. $29,440.00
2 $27,048.80
3 ?
(1 point) The value of the car after three years is $ (round your answer to the nearest cent)
Answers
GPT-4o mini
To find the value of the car after three years using the equation \( f(x) = 32,000(0.92)^x \), we need to calculate \( f(3) \).
First, we calculate \( f(3) \):
\[
f(3) = 32,000 \times (0.92)^3
\]
Now, let's calculate \( (0.92)^3 \):
\[
(0.92)^3 = 0.92 \times 0.92 \times 0.92 = 0.778688
\]
Next, substitute this value back into the equation:
\[
f(3) = 32,000 \times 0.778688
\]
Now, performing the multiplication:
\[
f(3) \approx 32,000 \times 0.778688 \approx 24,979.016
\]
Rounding to the nearest cent:
\[
f(3) \approx 24,979.02
\]
Thus, the value of the car after three years is approximately **$24,979.02**.
First, we calculate \( f(3) \):
\[
f(3) = 32,000 \times (0.92)^3
\]
Now, let's calculate \( (0.92)^3 \):
\[
(0.92)^3 = 0.92 \times 0.92 \times 0.92 = 0.778688
\]
Next, substitute this value back into the equation:
\[
f(3) = 32,000 \times 0.778688
\]
Now, performing the multiplication:
\[
f(3) \approx 32,000 \times 0.778688 \approx 24,979.016
\]
Rounding to the nearest cent:
\[
f(3) \approx 24,979.02
\]
Thus, the value of the car after three years is approximately **$24,979.02**.