Question: A particular stock has value V(t) at time t where V (t) = \(K{{e}^{\sqrt{t}}}\) , where K > 0 . Assume that alternative investments grow in value according to \({{e}^{rt}}\) . Calculate the instantaneous rate of change in the value of the stock. Calculate the instantaneous rate of change in the value of alternative investments. What is the optimal time to sell the stock?

Now suppose K = 10 and r = .10. What is the optimal time to sell the stock? Confirm your answer by doing the following: (1) Create a spread sheet in Excel with Column A consisting of the integers from 1 to 50 which denote years. In Column B, evaluate the appropriate present value function for the present value of the stock at all of the years in Column A. Use the graphing tool in Excel to graph the function with years on the horizontal axis and the present value function on the vertical axis. Does it reach a maximum at the correct number of years?

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