Suppose that t years from now, one investment plan will be generating profit at

Question

Suppose that t years from now, one investment plan will be generating profit at the rate of P'1(t)=100+t^2 hundred dollars per year, while the second investment will be generating profit at the rate of P' 2(t)=220+2t hundred dollars per year.

a)For how many years does the rate of profitability of the second investment exceed that of the first?
b)Comptue the net excess profit assuming that you invest in the 2nd plan for the time period determined in part a.
c)Sketch teh rate of profitaility curves y=P ' 1(t) and y=P ' 2(t) and shade the region whose area represents the net excess profit from part b

Explanation / Answer

here i solved it for you

Graphing both equations, for 12 years second investment exceeds the first.
or
100+t^2 < 220+2t
t^2-2t-120 < 0
(t-12)(t+10) < 0
t < 12
when t=13 or more (t-12)(t+10) > 0

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