Suppose that there is a function that accepts an array as a parameter. When called with an

array of length $0,$ it executes $8$ instructions. When called with an array of length $n>0,$ it

executes $8n+64$ instructions, and two recursive function calls with an array size of $n-$

includes everything except the instructions executed during the recursive

calls.$)$ Prove that this function executes $88(2^n)-8n-80$ instructions when its input has

length $n,$ for all $n0.$

Suppose that DivisionMystery is a function that accepts an integer $n$ as a parameter. When

called with $n=1,$ it executes $2$ instructions. When called with a larger value of $n,$ it

executes $10n+30$ instructions and two recursive calls to DivisionMystery$(\frac{n}{2}).$ Prove,

by induction, that DivisionMystery $(n)$ executes $10nlgn+32n-30$ instructions for all

$n1.$ Note: we use $lgn$ to represent the $log$ base $2$ of $n($i$.$e$.,lo{g}_{2}n).$