$[2]$ Give a Turing machine $M$ such that

i$.$ its input alphabet is $0,1$ ;

ii$.,M$ accepts an input string $s$ if and only if $s$ contains twice as many $0$ s as it contains $1s.$

What is the runtime of your TM$?$

You can define $M$ either by the table of its transition function, or by a labeled graph, or by giving precise

description of its operation in plain English.$[2]$ Take the following list of functions and arrange them in the order of growth rate:

$n^{2\mathrm{.}5},\sqrt[\phantom{2}]{2n},n+10,{10}^n,{100}^n,n^{2logn}$