$\begin{align*} &\Rightarrow T(N) - T(N-1) = 2^{N} \\\\ &\Rightarrow \text{Adding summation to the both sides,} \\\\ &\Rightarrow \sum_{N=1}^{N=N}T(N) - T(N-1) = \sum_{N=1}^{N=N} 2^{N}\\ \\ &\Rightarrow T(N) - T(0) = 2^{1} + 2^{2} + 2^{3} + ............ + 2^{N}\\\\ &\Rightarrow T(N) - T(0) = 2^{N+1} -2\\\\ &\Rightarrow T(N) - T(0) = O(2^{N})\\ \end{align*}$