Question
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.
Table:
x f(x)
0 32,000
1 29,440
2 27,084.80
3 ?
x
. Complete the table to find the value of the car to the nearest cent after three years.
Table:
x f(x)
0 32,000
1 29,440
2 27,084.80
3 ?
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 calculate \( f(3) \).
\[
f(3) = 32,000(0.92)^3
\]
First, calculate \( (0.92)^3 \):
\[
(0.92)^3 = 0.778688
\]
Now, multiply this value by 32,000:
\[
f(3) = 32,000 \times 0.778688 \approx 24,971.00
\]
So, the value of the car after three years, to the nearest cent, is:
\[
f(3) \approx 24,971.00
\]
Now, we can complete the table:
| x | f(x) |
|---|-----------|
| 0 | 32,000.00 |
| 1 | 29,440.00 |
| 2 | 27,084.80 |
| 3 | 24,971.00 |
\[
f(3) = 32,000(0.92)^3
\]
First, calculate \( (0.92)^3 \):
\[
(0.92)^3 = 0.778688
\]
Now, multiply this value by 32,000:
\[
f(3) = 32,000 \times 0.778688 \approx 24,971.00
\]
So, the value of the car after three years, to the nearest cent, is:
\[
f(3) \approx 24,971.00
\]
Now, we can complete the table:
| x | f(x) |
|---|-----------|
| 0 | 32,000.00 |
| 1 | 29,440.00 |
| 2 | 27,084.80 |
| 3 | 24,971.00 |