After how many years will the population be growing at 2,000 people per year?

Explanation

1. 01

   $P'(t) = 1000\,e^{0.02t} = 2000$ gives $e^{0.02t} = 2$.

2. 02

   $0.02t = \log 2$, so $t = 50\log 2 \approx 34.7$ years.