Question
11. 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 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.
x f(x)
0 32,000
1 29,440
2 27,048.80
3 ?
(1 point)
The value of the car after three years is $
(round your answer to the nearest cent)
.
If the car depreciates in a 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.
x f(x)
0 32,000
1 29,440
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 given model \( f(x) = 32,000(0.92)^x \), we can substitute \( x = 3 \) into the equation.
\[
f(3) = 32,000(0.92)^3
\]
Now, first we need to calculate \( (0.92)^3 \):
\[
(0.92)^3 = 0.778688
\]
Now multiply this result by 32,000:
\[
f(3) = 32,000 \times 0.778688 \approx 24,973.96608
\]
Rounding this to the nearest cent gives:
\[
f(3) \approx 24,973.97
\]
Therefore, the value of the car after three years is \( \text{\$} 24,973.97 \).
\[
f(3) = 32,000(0.92)^3
\]
Now, first we need to calculate \( (0.92)^3 \):
\[
(0.92)^3 = 0.778688
\]
Now multiply this result by 32,000:
\[
f(3) = 32,000 \times 0.778688 \approx 24,973.96608
\]
Rounding this to the nearest cent gives:
\[
f(3) \approx 24,973.97
\]
Therefore, the value of the car after three years is \( \text{\$} 24,973.97 \).