A new car that costs $15,000 depreciates 21% each year. Write a function to model the value of the care after t amount of years. (2 points)

Answer 1

To model the depreciation of a car's value over time, we can use the formula for exponential decay. The value of the car after \( t \) years can be modeled using the formula:

\[ V(t) = V_0 \times (1 - r)^t \]

Where:

• \( V(t) \) is the value of the car after \( t \) years.
• \( V_0 \) is the initial value of the car (in this case, $15,000).
• \( r \) is the rate of depreciation (21% or 0.21).
• \( t \) is the number of years.

Given this information, we can write the function in a programming language like Python:

def car_value(t):
    V0 = 15000  # initial value of the car
    r = 0.21    # depreciation rate
    V_t = V0 * (1 - r) ** t  # value after t years
    return V_t

In this function, you can call car_value(t) where t is the number of years, and it will return the value of the car after that many years.