Arrange the functions below in non-decreasing order such that if f_i appears before f_i, then f_i(n) elementof O(f_j(n)). f_1(n) = 10^20 f_2(n) = (lgn)^4 f_3(n) = 4^n f_4(n) = n lg n f_5(n) = n^3 - 100n^2 f_6(n) = n + lg n f_7(n) = lg lg n f_8(n) = n^0.1 f_9(n) = lg n^5 Group the following functions into classes so that two functions f(n) and g(n) are in the same class if and only if f(n) elementof theta (g(n)). List the classes in increasing order of magnitude of its members. A class may consist of one or more members. f_1(n) = 600 f_2(n) = (lg n)^6 f_3(n) = 3^n f_4(n) = lg n f_5(n) = n + lg n f_6(n) = n^3 f_7(n) = n^2 lg n f_8(n) = n^2 - 100 f_9(n) = 4n + squareroot n f_10(n) = lg lg n^2 f_11(n) = n^0.3 f_12(n) = n^2 f_13(n) = lg n^2 f_14(n) = squareroot n^2 + 4 f_15(n) = 2^n