$T(0) = 1 = $ $2^{0} $
$T(1) = 2T(0) = 2 = $$ 2^{1} $
$T(2) = 2 T(1) = 2.2 = $ $2^{2} $
$T(3) = 2 T(2) = 2.2.2= $ $2^{3} $
$.......$
$T(n) = 2T(n-1) = 2.2.2.2.2....n times =$ $ 2^{n} $
$\therefore T(n) = O(2^{n})$
Hence Option C is the correct answer.