Which function grows faster, exponential or factorial?

n! = n * (n-1) * (n-2) * ...

n^n = n * n * n * ...

Every term after the first one in n^n is larger, so n^n will grow faster.

n! eventually grows faster than an exponential with a constant base (2^n and e^n), but n^n grows faster than n! since the base grows as n increases.