The predicted value of the car in 1998, based on the calculated exponential depreciation model, is approximately $5,621.18, rounded to the nearest dollar.
We can predict the car's value in 1998:
1. Calculate the depreciation rate:
We know the initial value in 1992 was $28,000 and the value dropped to $9,600 in 1996, a period of 4 years.
This represents a decrease of $18,400 in value over 4 years.
Therefore, the annual depreciation rate is $18,400 / 4 years = $4,600 per year.
2. Model the car's value as an exponential function:
The car's value depreciates exponentially, meaning the rate of decrease remains constant over time.
We can model this using an exponential function of the form:
V(t) = V_0 * e^(-r * t)
Where:
V(t) is the car's value at time t (years since 1992)
V_0 is the initial value ($28,000)
r is the depreciation rate ($4,600 per year)
3. Predict the value in 1998:
We want to find V(6), where t = 6 represents 1998 (6 years after 1992).
Plugging in the values, we get:
V(6) = 28,000 * e^(-4,600 * 6) ≈ $5,621.18
Therefore, the predicted value of the car in 1998 is approximately $5,621.18, rounded to the nearest dollar.