Rank the following functions by order of asymptotic growth r

Rank the following functions by order of asymptotic growth rate. If two functions have the same asymtotic growth, provide an explanation.

n 5, logon), 100100 1, n log(Ta) Ti log(Ti 2n, Tl 2n. Tl 100 12),

Solution

Let us first group them

Constant : 2^n, 2^2n ,100^100 ,1
Logarithmic : log(n)
Linear: n+5
nlog(n), nlog(n^2)
Polynomial : n^100
n!

Now order of increasing rank is
1, 100^100, 2^n , 2^2n , log(n), n+5 , nlog(n^2) , n^100 , n!