Growth rate of $n3^n$ vs $4^n$

Question

Does the latter grow faster? I'm assuming that if we have $a^n$ vs $b^n$, if $b>a$ then $a = O(b)$, but if there is a n term in front of a does that change it?

Answer 1

Note that for suitably large $n$ we have $n << (4/3)^n$. This shows directly that $4^n$ grows faster.