anonymous
  • anonymous
A population of a small town in North Dakota fits the model P(t)=1500e^-0.35(t) with t=0 corresponding to 1998. When will the last person leave this town?
Mathematics
chestercat
  • chestercat
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Rogue
  • Rogue
We can't solve for P (t) = 0, so I'm pretty sure the question is asking us to solve for P (t) < 0.5.\[0.5 < 1500e ^{-0.35t}\]\[(1/3000) < e ^{-.35t}\]\[t = (\ln 3000)/0.35 \approx 22.875 years\] Add that to 1998, and we get that the last person will leave on 2020.

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