Differentiate p with respect to t, set the derivative equal to 0, and solve for t.
As the financial consultant to a classic auto dealership, you estimate that the total value (in dollars) of its collection of 1959 Chevrolets and Fords is given by the formula
v = 305,000 + 970t^2 (t ≥ 5)
where t is the number of years from now. You anticipate a continuous inflation rate of 5% per year, so that the discounted (present) value of an item that will be worth $v in t years' time is
p = ve^−0.05t.
How many years from now would you advise the dealership to sell the vehicles to maximize their discounted value?