Overview
I'm working on a mathematics question and need an explanation and answer to help me learn.
Software packages A and B of complexity O(n log n) and O(n), respectively, spend exactly TA(n) = cAn log10 n and TB(n) = cBn milliseconds to process n data items. During a test, the average time of processing n = 104 data items with the package A and B is 100 milliseconds and 500 milliseconds, respectively. Work out exact conditions when one package actually outperforms the other and recommend the best choice if up to n = 109 items should be processed