Your task in this exercise is to put the following functions into their appropriate positions in the list so that finally the list will

contain all the functions in ascending order of their growth rates. You can swap two functions by clicking on them.

$nloglogn,lo{g}^{2}n,7\sqrt[\phantom{2}]{n},n^{\frac{4}{3}},n^2,2^{n^2}$

Constant terms never matter, so ignore something like multiplying by $9.$

Focus on the exponent.

Generally, things that are only logs go first. Note that $loglogn($taking the $log$ of $logn)$ grows slower than $lo{g}^{2}n$

$($multiplying $logn$ by itself$).$

Generally, constant powers of $n$ come after things with only log factors. Even a small constant power of $n$ grows faster

than things with only logs$.$ So $\sqrt[\phantom{2}]{n}$ grows faster than $lo{g}^{3}n.$

Generally, things with some function of $n$ in the exponent go last. These are called "exponentials". Of the

exponentials, just see what has the biggest function in the exponent. For example, since $\sqrt[\phantom{2}]{n}$ grows faster than

$logn,$ then $2^{\sqrt[\phantom{2}]{n}}$ grows faster than $2^{logn}.$