For each of the following pairs of functions, indicate whether the first function of each of the following pairs has a lower, same, or higher order of growth (to within a constant multiple) than the second function.
a. n(n + 1) and 2000n^2 b. 100n^2 and 0.01n^3
c. log2 n and ln n d. and log2 n^2
e. 2n−1 and 2^n f. (n − 1)! and n!
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