Final answer:
To find the predicted value of Jocelyn's car in 2012, we use the exponential decay formula to calculate the rate of depreciation and then apply it to find the future value, resulting in a predicted value of $2,915.
Step-by-step explanation:
To determine the predicted value of Jocelyn's car in the year 2012, we will use the exponential decay formula:
V = P * e(rt)
Where:
V is the future value of the car
P is the initial value of the car
e is the base of the natural logarithm
r is the rate of depreciation
t is the time in years
Given that the car's value went from $16,100 in 2000 to $8,500 in 2005, we first need to calculate the annual rate of depreciation:
8,500 = 16,100 * e(5r)
Solving for r, we find that r ≈ -0.1222 (rounded to four decimal places). Now, we can predict the value of the car 2012, which is 12 years after 2000.
V = 16,100 * e(-0.1222 * 12)
Calculating this, we get that the predicted value to the nearest dollar is $2,915.