$3(14$ pts$)$ Give a big$-$ bound for the solutions of the following relations $($show work$).$

$($a$)T(n)=T(n-1)+4$

$($b$)T(n)=4T(n-2)+3n$

$4($extra credit $2\mathrm{.}5$ pts $)$ Show that for any positive integer $n,$ there must be some power

of $2$ lying in the range $[n,2n).$