$1.)(20$ points$)$ If we have the recursive relation $T(n)=3T(\frac{n}{7})+Cn$ for $n>1($with base case $T(1)$ a constant$)$ defining ${?}^1$ a function $T(n)$ then there is some function in the $-$set hierarchy, $g(n),$ which makes $T(n)in(g(n))$ true. Use either expansion into a series or the recursion tree method to determine $($a$.$k$.$a$.$ guess$)$ what that function is$.$ Include your work.

Do NOT do the proof by substitution!