Question

A brand of cars wants to have an expression to determine how the price of its new model decreases with time. After applying an empirical study, they arrived at the expression: ( P = P_0 × e^-kt ), where ( P ) is the price after time ( t ), ( P_0 ) is the initial price, and ( k ) is a constant. True or False: This exponential expression models the price decrease of the new model over time.

Answer 1

The expression P = P_0 × e^-kt is True for modeling the exponential decrease in the price of a new car model over time, indicating that the car's value diminishes as time progresses.

Step-by-step explanation:

The student's question asks whether the expression P = P_0 × e^-kt accurately models the price decrease of a new car model over time. The answer is True. This equation represents an exponential decay model, where P is the price of the car after time t, P_0 is the initial price at time t=0, and k is a constant that determines the rate of depreciation. As time increases, e^-kt decreases since it's raised to a negative power, hence the overall product P, which is the price of the car, also decreases. This shows that as time goes on, the value of the car diminishes exponentially.