The value of John's car depreciates 20 percent per year. What is the equation and is it a linear or exponential model?
The equation for the depreciation of John's car can be represented as:
V = P * (1 - r)^t
Where:
V = Value of the car after t years
P = Initial value (purchase price) of the car
r = Depreciation rate (20% or 0.20)
t = Number of years
This equation represents an exponential model because the value of the car is decreasing by a fixed percentage each year.
To find the equation that represents the depreciation of John's car, we can use the general formula for exponential decay:
P(t) = P₀ * (1 - r)^t
Where:
P(t) - represents the value of the car after 't' years
P₀ - represents the initial value of the car
r - represents the rate of depreciation (as a decimal)
t - represents the number of years
In this case, the car depreciates 20 percent per year, which means the rate of depreciation 'r' is 0.20. If we assume the initial value of John's car is 'V₀', the equation becomes:
P(t) = V₀ * (1 - 0.20)^t
Simplifying further:
P(t) = V₀ * (0.80)^t
This equation represents an exponential model because the value of the car after each year is multiplied by the constant factor of 0.80 (1 - 0.20). The decrease is not a constant amount but rather a percentage of the previous value. Therefore, it follows an exponential decay pattern.
after n years value = original price * 0.8^n
.8^n is not linear :)