sec exercises arrange the following expressions by growth rate from slowest to fastest log log / see stirling' approximation in section for help in classifying (asuppose that particular algorithm has time complexity ( and that executing an implementation of it on particular machine takes seconds for inputs now suppose that we are presented with machine that is times as fast how many inputs could we process on the new machine in seconds(bsuppose that another algorithm has time complexity (nn and that executing an implementation of it on particular machine takes seconds for inputs now suppose that we are presented with machine that is times as fast how many inputs could we process on the new machine in seconds(ca third algorithm has time complexity ( executing an implementation of it on particular machine takes seconds for inputs given new machine that is times as fasthow many inputs could we process in seconds hardware vendor xyz corp claims that their latest computer will run times faster than that of their competitorprunesinc if the prunesinc computer can execute program on input of size in one hourwhat size input can xyz' computer execute in one hour for each algorithm with the following growth rate equationsn (afind growth rate that squares the run time when we double the input size that isif (nxthen ( nx (bfind growth rate that cubes the run time when we double the input size that isif (nxthen ( nx using the definition of big-ohshow that is in ( and that is in ( using the definitions of big-oh and ohmfind the upper and lower bounds for the following expressions be sure to state appropriate values for and (ac (bc (cc log (dc (awhat is the smallest integer such that (nk )