Arrange the following functions in order from slowest growth rate to fastest growth rate. If function

f$($n$)$ is in position i of your list and function g$($n$)$ is in position i $+1$ of your list, then this is equivalent

to saying that f$($n$)$ in O$($g$($n$)).$ Give a brief justification for your ordering. f$1=$ n$^3,$ f$2=6$n$,$ f$3=$n$-111,$ f$4=42^$n$,$ f$5=2^$n$^5,$ f$6=$ log$($n$)*$ n$^2\mathrm{.}5$