Question
Question:
A new car that costs $15,000 depreciates 21% each year. Write a function to model the value of the car after t amount of years.
A new car that costs $15,000 depreciates 21% each year. Write a function to model the value of the car after t amount of years.
Answers
Answered by
GPT-4o mini
To model the value of the car after \( t \) years given that it depreciates by 21% each year, you can use an exponential decay formula. The formula to calculate the value of the car after \( t \) years can be expressed as:
\[
V(t) = P \times (1 - r)^t
\]
Where:
- \( V(t) \) is the value of the car after \( t \) years.
- \( P \) is the initial price of the car (which is $15,000).
- \( r \) is the rate of depreciation (which is 21%, or 0.21 as a decimal).
- \( t \) is the number of years.
Given this, the function to model the value of the car can be written in Python as follows:
```python
def car_value_after_years(initial_price, depreciation_rate, years):
return initial_price * (1 - depreciation_rate) ** years
# Constants
initial_price = 15000 # Initial cost of the car
depreciation_rate = 0.21 # 21% depreciation rate
# Example usage
years = 5 # For example, calculating the value after 5 years
value_after_years = car_value_after_years(initial_price, depreciation_rate, years)
print(f"The value of the car after {years} years is: ${value_after_years:.2f}")
```
This function takes the initial price, the depreciation rate, and the number of years as inputs, and it returns the value of the car after the specified number of years.
\[
V(t) = P \times (1 - r)^t
\]
Where:
- \( V(t) \) is the value of the car after \( t \) years.
- \( P \) is the initial price of the car (which is $15,000).
- \( r \) is the rate of depreciation (which is 21%, or 0.21 as a decimal).
- \( t \) is the number of years.
Given this, the function to model the value of the car can be written in Python as follows:
```python
def car_value_after_years(initial_price, depreciation_rate, years):
return initial_price * (1 - depreciation_rate) ** years
# Constants
initial_price = 15000 # Initial cost of the car
depreciation_rate = 0.21 # 21% depreciation rate
# Example usage
years = 5 # For example, calculating the value after 5 years
value_after_years = car_value_after_years(initial_price, depreciation_rate, years)
print(f"The value of the car after {years} years is: ${value_after_years:.2f}")
```
This function takes the initial price, the depreciation rate, and the number of years as inputs, and it returns the value of the car after the specified number of years.