Question 1186430
A) To find the annual rate of change, we can use the formula for exponential decay:

```
Final Value = Initial Value * (1 - r)^t
```

Where:

* Final Value = $12,000
* Initial Value = $27,000
* r = annual rate of change (what we want to find)
* t = number of years = 2001 - 1994 = 7

Let's plug in the values and solve for r:

```
12000 = 27000 * (1 - r)^7
(12000/27000) = (1 - r)^7
(4/9) = (1 - r)^7
(4/9)^(1/7) = 1 - r
r = 1 - (4/9)^(1/7)
r ≈ 0.1094
```

Therefore, the annual rate of change is approximately **0.1094**.

B) To express the rate in percentage form, we simply multiply by 100:

```
r ≈ 0.1094 * 100 = 10.94%
```

Therefore, the annual rate of change is approximately **10.94%**.

C) To find the value in 2006, we can use the same formula, but with t = 2006 - 1994 = 12:

```
Value in 2006 = 27000 * (1 - 0.1094)^12
Value in 2006 ≈ 6715.64
```

Rounding to the nearest 50 dollars, the value of the car in 2006 will be approximately **$6700**.