You purchased a new car for $22,000. The value of the car decreases by 15% each year. Which function could be used to model the value of the car, "V", after "t" years?

15% loss means each year the value is 0.85 what it was.

To model the value of the car after "t" years, we can use the formula for exponential decay, which is given by:

V = P(1 - r)^t

Where:
V represents the value of the car after "t" years
P represents the initial purchase price of the car ($22,000)
r represents the rate of decrease (15% or 0.15 as a decimal)
t represents the number of years

Using this formula, the function that could be used to model the value of the car after "t" years is:

V(t) = 22,000(1 - 0.15)^t

To model the value of the car after a certain number of years, you can use an exponential decay function. The general form of an exponential decay function is:

V = P * (1 - r)^t

Where:
V represents the value of the car after t years
P represents the initial value or purchase price of the car
r represents the rate of decay as a decimal (in this case, 15% or 0.15)
t represents the number of years elapsed since the purchase

In this scenario, you purchased the car for $22,000, and it depreciates by 15% each year. Therefore, you can use the exponential decay model with the given values:

V = 22000 * (1 - 0.15)^t

Simplifying the equation, you get:

V = 22000 * 0.85^t

So, the function that can be used to model the value of the car, V, after t years is V = 22000 * 0.85^t.