Arrange the following expressions by growth rate from slowest to fastest. 4 n 2 4n2 t log

Arrange the following expressions by growth rate from slowest to fastest.

• $4n^2$${\log }_{3}n$$n!$$3^n$$20n$$2$${\log }_{2}n$$n^{2/3}$

See Stirling’s approximation in Section 2.2 for help in classifying $n!$.

Data From Section 2.2:

Stirling’s approximation states that:

where e ≈ 2.71828 (e is the base for the system of natural logarithms). Thus we see that while n! grows slower than nⁿ (because √ 2πn/eⁿ n for any positive integer constant c.