Order of growth

Question

Arrange the following functions in ascending order according to their order of growths.

$$\begin{align}
f_1 &= 100000 \cdot n\\[1em]
f_2 &= \frac1{30} \cdot n^2\\[1em]
f_3 &= (\log n)^{200}\\[1em]
f_4 &= 2^n\\[1em]
f_5 &= n \cdot \log n
\end{align}$$

Answer 1

f1 (linear) < f5 (log linear * linear) < f2 (quadratic) < f4 (exponential)

Now, f3 is actually growing smaller than $n$. For example, take $n=2^{2^{16}} = 2^{65536}, {\log_2 n}^{200} = \left({2^{16}}\right)^{200} = 2^{3200}$.For all larger $n$, f3 has lower value than $n$.   (This is true for $\log n^k$ for any constant $k$. So,

$$f3 < f1 < f5 < f2 < f4.$$