TITLE: Functions between polynomial and exponential
QUESTION [8 upvotes]: Does there exist a function $f(n)$ such that as $n \rightarrow \infty$, we have $p(n) < f(n) < e(n)$? Where $p$ is any polynomial and $e$ is any exponential (e.g. $e(n) = e^{\alpha n}, \alpha > 0$)

REPLY [8 votes]: How about $f(n)=e^{\sqrt{n}}$, slowing down the exponent in $e^n$? Or $f(n)=n^{\log{n}}$, speeding up the exponent in $n^k$?