Polynomials with $\textrm{degree}>1$ grow faster than arithmetic sequences but slower than geometric sequences.
More generally, after sufficiently many terms:
\begin{align*} & \textrm{logarithm}(n) \\ & \lll \textrm{radical}(n) \\ & \lll \textrm{linear}(n) \\ & \lll \textrm{polynomial}(n) \\ & \lll \textrm{exponential}(n) \\ & \lll \textrm{factorial}(n) \end{align*}
For example, consider the following sequences:
\begin{align*} \log_{2} n \lll \sqrt{n} \lll n \lll n^2 \lll 2^{n} \lll n! \end{align*}
Substituting $n=1000,$ we get
\begin{align*} & \log_{2}{1000} \approx 10 \\ & \lll \sqrt{1000} \approx 32 \\ & \lll 1000 = 10^3 \\ & \lll 1000^2 = 10^6 \\ & \lll 2^{1000} \approx 10^{301} \\ & \lll 1000! \approx 10^{2567} \end{align*}