Consider the following recurrence relation:

$T(n)=\{\begin{array}{ccc}{c}_0,& if& n=1\\ \sqrt[\phantom{2}]{2}T(\frac{n}{2})+c_1,& if& n>1\end{array}$

What is the tightest complexity class that you can attribute to this recurrence relation?

$T(n)=(\sqrt[\phantom{2}]{n})$

$T(n)=O(\sqrt[\phantom{2}]{n})$

$T(n)=(lo{g}_{2}n)$

$T(n)=(nlo{g}_{2}n)$

$T(n)=(n^2)$