I am supposed to arrange the functions into increasing order of growth rates.
$$3^n, 2^n, n2^n, n^{30}, (\log n)^3, \sqrt{n}\log^2 n, n\log n, \sqrt{n!}, n^{29}+n^{27}, n^{2\sqrt{n}}$$
I came up with the following
$$(\log n)^3 < \sqrt{n}\log^2 n < n\log n < n^{29}+n^{27} < n^{30} < 2^n < n2^n < 3^n < n^{2\sqrt{n}} < \sqrt{n!}$$
However, I am not confident in my answer and was looking for feedback. Did I do it right?