Take the following list of functions and arrange them inascending order of growt

Question

Take the following list of functions and arrange them inascending order of growth rate. That is, if function g(n)immediately follows function f(n) in your list, then it should bethe case that f(n) is O(g(n)).

               f1(n) = n2.5

               f2(n) = sqrt(2n)

               f3(n) = n + 10

               f4(n) = 10n

               f5(n) = 100 n

               f6(n) = n 2 log n

Justify your ordering of the functions.

Explanation / Answer

We know that: 1) 10n < 102n   i.e10n n2 log n for n>1 3) sqrt(2n) n+10 for n> 4 5) 10n > n2.5 for n> 1 Therefore the ascending order [for sufficiently large values of n]of the function that satisfy the given question is: 1) sqrt (2n) 2) n + 10 3) n2 log n 4) n2.5 5) 10n 6) 100n

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