In general we say that polynomials grow faster than linear functions. but take the following functions, we have that log^3(n) = o(n). here the linear term grows much faster. however, when we increase the power we get the opposite, e. g. n = o(log^7( where the log term grows faster. how can i determine where the limit lies (or where the equality shifts) for such cases? are there general guidelines to follow?

Write a program that keeps asking the user for new values to be added to a list until the user enters 'exit' ('exit' should not be added to the list). these values entered by the user are added to a list we call 'initial_list'. then write a function that takes this initial_list as input and returns another list with 3 copies of every value in the initial_list. finally, inside print out all of the values in the new list. for example: input: enter value to be added to list: a enter value to be added to list: b enter value to be added to list: c enter value to be added to list: exit output: a b c a b c a b c note how 'exit' is not added to the list. also, your program needs to be able to handle any variation of 'exit' such as 'exit', 'exit' etc. and treat them all as 'exit'.