2. (25 points) You have just bought a painting at a price of K >0. Its value grows continuously over time at a rate of 47 where t is time counted from today. The continuously accruing profit rate on your best alternative investment is equal to r>0. a) Write down the present discounted value of your painting as a function of time. b) Find how long you should keep the painting in order to maximize the present discounted value of your assets. c) Explain the economic intuition of your answer in part b) d) Show that your answer in part b) is, in fact, the holding period that maximizes the present discounted value of your wealth.