Problem $3.[10$ points$]$ Give the asymptotic running time of the following algorithm in $\backslash$Theta

notation. Briefly justify your answer. Be sure to justify both the upper and the lower bound.

Func$1($n$)$

$1$ s $0$;

$2$ i $5$;

$3$ while $($i $$ n$2+7)$ do

$4$ for j $$ i to i

$3$

log i do

$5$ s $$ s $+1$;

$6$ end

$7$ i $$ i $\backslash$times $4$;

$8$ end