Suppose that t years from now, one investment plan will be generating profit at the rate of P₁ (t) = 60e0.0⁹t thousand dollars per year, while a second investment will be generating P₂(t) = 130e0.05t thousand dollars per year. a. For how many years does the rate of profitability of the second investment exceed that of the first? Answer: b. Compute the net excess profit, in thousands of dollars, assuming that you invest in the second plan for the time period determined in part a. Answer: c. Sketch the rate of profitability curves y = P₁ (t) and y = P₂ (t) and shade the region whose area represents the net excess profit computed in part b. There is nothing to submit here unless your instructor asks for your sketch.