Question
Use the table to answer the question.
x f(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
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 $.
x f(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
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 $.
Answers
GPT-4o mini
To find the value of the car after three years using the depreciation model \( f(x) = 32,000(0.92)^x \), we can substitute \( x = 3 \) into the equation:
\[
f(3) = 32,000(0.92)^3
\]
First, calculate \( (0.92)^3 \):
\[
(0.92)^3 = 0.778688
\]
Now, substitute this back into the equation:
\[
f(3) = 32,000 \times 0.778688
\]
Now perform the multiplication:
\[
f(3) \approx 32,000 \times 0.778688 \approx 24,964.00
\]
Therefore, the value of the car after three years is approximately **$24,964.00**.
\[
f(3) = 32,000(0.92)^3
\]
First, calculate \( (0.92)^3 \):
\[
(0.92)^3 = 0.778688
\]
Now, substitute this back into the equation:
\[
f(3) = 32,000 \times 0.778688
\]
Now perform the multiplication:
\[
f(3) \approx 32,000 \times 0.778688 \approx 24,964.00
\]
Therefore, the value of the car after three years is approximately **$24,964.00**.