Question

Arrange the following functions in order of non-decreasing growth rate; i.e., fi may precede only if fi = 0(f; ). There is no need to show proof of the ordering. f1(n) = n2 f2(n) = V100 f3(n) = n + 10 f4(n) = 2n f5(n) = 10" f6(n) 2n log n f7(n) = log log n f8(n) = 2logn f9(n)=2¹⁰⁰

Answer 1

The functions are ordered from slowest to fastest growth rate as follows: log log n, square root of 100, 2 raised to the power of 100, 2 times the logarithm of n, n plus 10, 2 times n, 2 times n logarithm n, n squared, and 10 raised to the power of n.

Step-by-step explanation:

To arrange the given functions in order of non-decreasing growth rate, we need to understand the rate at which each function increases as the input variable n becomes large. Here is the ordered list:

1. f7(n) = log log n
2. f2(n) = √100
3. f9(n) = 2¹100
4. f8(n) = 2log n
5. f3(n) = n + 10
6. f4(n) = 2n
7. f6(n) = 2n log n
8. f1(n) = n²
9. f5(n) = 10ⁿ

In this list, logarithmic functions precede constant functions, which precede polynomial functions. The functions are ordered from slowest growth to fastest growth rate.