Question: Suppose that t years from now, one investment plan will be generating profit at the rate of \({{P}_{1}}'\left( t \right)=100+{{t}^{2}}\) hundred dollars per year, while a second investment will be generating profit at the rate of \({{P}_{2}}'\left( t \right)=200+2t\)

hundred dollars per year.

1. For how many years does the rate of profitability of the second investment exceed that of the first?
2. Compute the net excess profit assuming that you invest in the second plan for the time period determined in part (a)

Sketch the rate of profitability curves \(y={{P}_{1}}'\left( t \right)\) and \(y={{P}_{2}}'\left( t \right)\) and shade the region whose area represents the net excess profit computed in part (b)

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