Final answer:
The formulas listed in order from greatest to least time requirements are: n^2 + 1, 10n + 10,000, 50 log n, and 1,000,000. The quadratic term grows the fastest, followed by the linear and logarithmic terms, with the constant term having no growth.
Step-by-step explanation:
To list the given formulas in order of running time analysis from greatest to least time requirements, assuming that n is very large, we compare the growth rates of the functions as n increases. When n is large, the polynomial n2 grows faster than linear terms, logarithmic terms, or constant terms. Therefore, the order from greatest to least is:
- n2 + 1
- 10n + 10,000
- 50 log n
- 1,000,000
The quadratic term n2 has the highest growth rate, followed by the $linear term 10n + 10,000. The logarithmic term 50 log n has a slower growth rate compared to the linear term, and the constant term 1,000,000 does not grow as n increases.