Note: For Problem $1$ only, no proofs needed. Consider the following functions: $$ a$($n$)=3$n$^2+7$ b$($n$)=7$n log n $$ c$($n$)=3^$n $$ d$($n$)=2$ n $+400,000$ e$($n$)=10$n$^240$ f$($n$)=$ log log n $$ g$($n$)=2$n$^(2/3)$ log$^2($n$)$ h$($n$)=2$ n $$ i$($n$)=$ n$!$ j$($n$)=$ e$^$n $$ n$^23$ k$($n$)=2^(2^$n$)$ l$($n$)=$ n$^($log n$)$ a$)$ Order these functions from left to right so that a $$ b means O$($a$($n$))$ O$($b$($n$)).$ For example, you might write a $$ b $$ c $$ d $$ e $$ f $$ g $$ h $$ i $$ j $$ k $$ l but of course that$$s not the right answer. What is$?$ b$)$ A function is called super$-$polynomial if it is not O$($n k $)$ for some constant k$.$ Which of the functions listed above are super$-$polynomial? c$)$ A function is called sub$-$exponential if it runs in time $2$o$($n$).$ Which of the functions would you describe as sub$-$exponential?