Question

A vehicle purchased for $25,000 depreciates at a constant rate of 6%. Determine the approximate value of the vehicle

11
years after purchase. Round to the nearest whole dollar.

Answer 1

To determine the approximate value of the vehicle 11 years after purchase, we can use the following formula for exponential decay:

V = V0 * (1 - r)^t

where:
V0 is the initial value of the vehicle (in dollars)
r is the depreciation rate (as a decimal)
t is the time elapsed (in years)
V is the current value of the vehicle (in dollars)

In this case, V0 = $25,000, r = 0.06 (since the vehicle depreciates at a constant rate of 6%), and t = 11 years. Substituting these values into the formula, we get:

V = $25,000 * (1 - 0.06)^11
V ≈ $11,295

Rounding to the nearest whole dollar, the approximate value of the vehicle 11 years after purchase is $11,295

Answer 2

Answer: The approximate value of the vehicle after one year is $23,500

Explanation:

This is because the 6% depreciation rate means that the vehicle loses 6% of its original value each year. In this case, 6% of $25,000 is $1,500, so the value of the vehicle after one year is $25,000 - $1,500 = $23,500.