Data Structures, Algorithms, & Applications in C++
Chapter 3, Exercise 19

(a)

Program A is faster than program B when 1000n < 10n², that is when n > 100.

(b)

Program A is faster than program B when 2n² < n³, that is when n > 2.

(c)

Program A is faster than program B when 2ⁿ < 100n, that is when n < 10.

(d)

Program A is faster than program B when 1000n log₂n < n², that is when n > 1000 log₂n. The switchover point is between 2¹³ and 2¹⁴.