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Power Seriesmedium
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A population grows according to P(t)=1000e0.05tP(t) = 1000 e^{0.05t}P(t)=1000e0.05t, where ttt is time in years. For small ttt, approximate P(t)P(t)P(t) using the degree-2 Maclaurin polynomial and estimate the population at t=0.2t = 0.2t=0.2 years.