Rank the following functions by order of growth; that is, find an arrangement g1, g2, . . . , g8 of the functions satisfying g1 = (g2), g2 = (g3), . . . , g7 = (g8). Partition your list into equivalence classes such that functions f(n) and g(n) are in the same class if and only if f(n) = (g(n)).

n!, n³, lg²n, 2^{2^n}, 2^{lg n}, eⁿ, n, 2ⁿ

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