Rank the following functions by order of growth from low to

Rank the following functions by order of growth from low to high. If two or more are of the same order (f(n) and g(n) are in the same class if and only if f(n)= theta g(n)), group them together. No proofs are necessary. Verify that f(n) = O(g(n)) where f(n) = 10 times 2^n + 20 times 2^n an g(n) = n!. Show all steps.

Solution

3. a. The order from low to high is:

70 x log n

lg(lg n)

(ln n) + lg(lg n)

47n³ + lg n

3n³ + 6n

2ⁿ

2^n-3

n⁴¹³

(n+7)!

n! * 2⁸