In general, for any real a and b such that a > 1, . For a discussion about this, see StackExchange. In particular, answer #3 starting from "we need only look at " has a rigorous proof that as when c > 1.

The function f(n) = e^n describes a chain reaction while g(n) = n describes simple burning. I recommend playing with the graphs of e^n and n at large n to see just how much faster e^n grows.