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.
Just like the one I did for you below
x = 20,000 e^0.9 t
The value of a new car decreases 35% during the first year. Mr. LeMarr paid $25600 for a new car. The value of the car at the end of the first year is what? The answer is $10 140. I calculated $8960. I don"t understand how the answer is $10140. Thanks.
To write an exponential decay model for the value of the car, we can use the formula:
V = P(1 - r)^t
Where:
- V represents the value of the car after t years
- P is the initial purchase price of the car
- r is the rate of depreciation per year expressed as a decimal
- t is the number of years
In this case, the initial purchase price (P) of the car is $20,000, and the rate of depreciation (r) is 10% per year, or 0.10.
So, the exponential decay model for the value of the car would be:
V = 20,000(1 - 0.10)^t
To estimate the value of the car after one year, we can substitute t = 1 into the equation:
V = 20,000(1 - 0.10)^1
Simplifying the equation, we have:
V = 20,000(0.90)
V ≈ $18,000
Therefore, the estimated value of the car after one year is approximately $18,000.