Final answer:
To determine the value of a vehicle after a certain number of years with 7% depreciation, the exponential decay formula V = P(1 - r)^t is used where V represents the future value of the vehicle, P is the initial purchase price of $25,000, and r is the rate of 0.07 for 7% depreciation per year.
Step-by-step explanation:
The question asks us to calculate the approximate value of a vehicle after a certain number of years given an initial purchase price and a constant rate of depreciation. To find the value of the vehicle after each year, we can use the formula for exponential decay, which is:
V = P(1 - r)^t
Where V is the value after t years, P is the initial purchase price, and r is the depreciation rate.
Given:
- Initial Purchase Price (P) = $25,000
- Depreciation Rate (r) = 7% or 0.07
- Time (t) = Number of years
The value of the vehicle after t years is calculated by:
V = $25,000(1 - 0.07)^t
To find the vehicle's value after a specific number of years, you substitute t with the number of years and calculate V, rounding to the nearest whole dollar. Remember, this is an approximation, as real-world factors can affect depreciation.