2. (30 points)

Rank the following functions by order of growth, i.e., g_i = (g_i+1)

(Note: look carefully at the equation above and give the correct order):

1. n^2

2. n!

3. n^3

4. (log₂n)^2

5. log₂(n!)

6. n*2^n

7. 2^(log₂n)

8. n^(1/log₂n)

Justify your answer.