A bacteria culture grows at a rate proportional to its size and triples in 2 hours. By what factor has it grown after 6 hours?

Explanation

1. 01

   $\frac{dN}{dt} = kN$ gives $N = N_0e^{kt}$, and $e^{2k} = 3$.

2. 02

   After 6 hours: $e^{6k} = \left(e^{2k}\right)^3 = 27$.