Question

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?

Answer 1

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.