To help you better understand why the definition of Big-O is concerned only with the behavior of functions for large values ofn, choose two functions with different growth rates in which the faster...

To help you better understand why the definition of Big-O is concerned only with the behavior of functions for large values ofn, choose two functions with different growth rates in which the faster growing function is lower at small values ofn, but eventually becomes larger. Write a short program that periodically compares the values of the two functions and illustrates the point at which the faster growing function overtakes the slower growing one. As an example, consider the following two functions:

• 
  f(n) = 500n
  ²+ 15n+ 1000


• 
  g(n) = 2n
  ³
  

Shown below is a table of the values of both functions for small values ofn.

n     f(n)     g(n)



10    51150     2000

20   201300    16000

30   451450    54000

40   801600   128000

50  1251750   250000

60  1801900   432000

70  2452050   686000

80  3202200  1024000

90  4052350  1458000
100  5002500  2000000
110  6052650  2662000
120  7202800  3456000
130  8452950  4394000
140  9803100  5488000
150 11253250  6750000
160 12803400  8192000
170 14453550  9826000
180 16203700 11664000
190 18053850 13718000
200 20004000 16000000
210 22054150 18522000
220 24204300 21296000
230 26454450 24334000
240 28804600 27648000
250 31254750 31250000
260 33804900 35152000

Oncenreaches 260govertakesf.