Suppose that on a particular computer, an Algorithm A, with inputs of size n, runs in 10n^2 steps, and another Algorithm B runs in 60n lg n steps [Note: lg x = log2(x)]. For what values of positive integers n is Algorithm A better than Algorithm B? Show how you solved this problem in steps

Is 2^(n+1) = O(2^n )? Is 2^(2n) = O(2^n ) ? Show your work and explain