Question

Maji bought the car for $33,940. The value of the car is predicted to depreciate to $17,480 after 5 years. a. If Maji keeps the car for an additional 3 years ( 8 years total), predict the value of the car at the end of those 3 additional vears. assuming the value continues decreasing exponentially at the same rate?

Answer 1

Explanation:

To predict the value of the car at the end of three additional years, we can use exponential decay formula.The formula to calculate exponential decay is given by:A = P (1 - r)^tWhere, A = Final amountP = Initial amountr = Rate of decayt = Time elapsedTherefore, using the formula, we can calculate the value of the car after three years.A = P (1 - r)^tFinal amount, A = $17,480Initial amount, P = $33,940Time elapsed, t = 5 yearsRate of decay, r = (A/P)^(1/t) - 1r = ($17,480/$33,940)^(1/5) - 1r = 0.107 or 10.7%Substituting the values in the formula, we getA = $33,940 (1 - 0.107)^8A = $33,940 (0.893)^8A = $14,836.94Therefore, the predicted value of the car at the end of three additional years is $14,836.94.