Please Explain your simplifications. I would truly appreciate it. Thank you.

5. (10 points) Place these functions in order from slowest asymptotic growth to fastest asymptotic growth. You will want to simplify them algebraically before comparing them. Give a short justification (a proof is not necessary) of how you came to this ordering. The notation lg n stand for log2 n. = fo(n) fi(n) f2(n) = nigni 16'gn 32 n/5 = 8 n f3(n) (Ign In n+2021 ng - n6 + n4 33n -n2+1 = fa(n) f5(n) fo(n) fr(n) f:(n) fg(n) = In lnln n 2021 yn = n2021