Order the following functions by growth rate

Question

Order the following functions by growth rate (n, sqrt n, n^1.5, n^2, n logn, 3/n, n log logn, 2^n,6,n^3)

Answer 1

Choose some values of n, such as 1, 10, 100, 1000, etc. Then take each function and apply it to each value for n and compare the results.

For example, let's consider just n, sqrt n, and n²:

n sqrt n n^2

1 1 1

10 3.16 100

100 10 10000

1000 31.6 1000000

If we were just comparing these three functions using these values for n, the order would be sqrt n ≤ n ≤ n².