Arrange the following growth rates in increasing order O((35)^n),O(n^4),O(1),O(n^3 logn)

Question

I want to Arrange the following growth rates in increasing order

This order are following : O((35)^n),O(n^4),O(1),O(n^3 logn) Please give me idea how to arrange growth rates in increasing order

Answer 1

It's $$O(1), O(n^3 \log n), O(n^4), O(35^n).$$

As a rule of thumb: exponential beats polynomial beats logarithmic beats constant.

Answer 2

The order is $$O(1), O(n^3 \log n), O(n^4), O(35^n)$$

The reason is that $1<n^3 \log n<n^4<35^n$.