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 ?

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Answer Box:

The value of the car after three years is $ \boxed{\text{?}} $

Answer 1

To find the value of the car after three years, we can use the given equation \( f(x) = 32,000(0.92)^x \).

We already have calculated the values for \( x = 0 \), \( x = 1 \), and \( x = 2 \). We just need to compute for \( x = 3 \).

1. **Calculate \( f(3) \)**:
\[
f(3) = 32,000(0.92)^3
\]

First, calculate \( (0.92)^3 \):
\[
0.92^3 \approx 0.778688
\]

Next, multiply by 32,000:
\[
f(3) \approx 32,000 \times 0.778688 \approx 24,970.00
\]

Thus, the value of the car after three years is approximately \( 24,970.00 \).

### Completed Table:
| x | f(x) |
|---|-----------|
| 0 | 32,000.00 |
| 1 | 29,440.00 |
| 2 | 27,084.80 |
| 3 | 24,970.00 |

### Answer Box:
The value of the car after three years is \( \boxed{24,970.00} \).