Car depreciation- The value of a new car purchased for $20,000 decreases by 10% per year. Write an exponential decay model for the value of the car. Use the model to estimate the value after one year.
v = 20000 (1 - .10)^y
Write a function to model the depreciation in value for a car purchase at $20000
To write an exponential decay model for the value of the car, we can use the formula:
V(t) = V0 * (1 - r)^t
Where:
V(t) represents the value of the car after time t
V0 is the initial value of the car
r is the rate of decay per time period
t is the number of time periods
In this case, the initial value of the car is $20,000 and the rate of decay is 10% per year, or 0.1. So the exponential decay model for the value of the car becomes:
V(t) = 20,000 * (1 - 0.1)^t
To estimate the value after one year, we substitute t = 1 into the model:
V(1) = 20,000 * (1 - 0.1)^1
V(1) = 20,000 * 0.9
V(1) = 18,000
Therefore, the estimated value of the car after one year is $18,000.
To write an exponential decay model for the value of the car, we need to consider the initial value ($20,000) and the rate of decrease (10% per year).
The exponential decay formula is given by:
A = P(1 - r)^t
Where:
A is the final amount (value of the car after t years)
P is the initial amount (value of the car initially)
r is the decay rate
t is the time in years
In this case, the initial amount (P) is $20,000 and the decay rate (r) is 10% per year, which can be written as 0.10. We want to estimate the value after one year (t = 1).
Using the formula, we substitute the values:
A = 20,000(1 - 0.10)^1
Simplifying further:
A = 20,000(0.90)
Now, calculate the value after one year:
A = 18,000
Therefore, the estimated value of the car after one year is $18,000.