Answer:
Explanation:
To determine the approximate value of the vehicle 13 years after purchase, we can use the concept of exponential decay. The vehicle depreciates at a rate of 9% per year, which means its value decreases by 9% each year.
The formula for exponential decay is:
Value after time (V) = Initial value (V0) * (1 - r)^t
where:
V0 = Initial value (purchase price)
r = Depreciation rate (as a decimal)
t = Time in years
Given:
Initial value (V0) = $27,500
Depreciation rate (r) = 9% = 0.09
Time (t) = 13 years
Now, plug these values into the formula:
V = $27,500 * (1 - 0.09)^13
V = $27,500 * (0.91)^13
V ≈ $27,500 * 0.3535
V ≈ $9,785.75
The approximate value of the vehicle 13 years after purchase is around $9,785.75.