Evaluating $ \binom{n}{0} + 2 \binom{n}{1} + 2^2 \binom{n}{2} + \dots + 2^k \binom{n}{k} + \dots + 2^n \binom{n}{n} $

Question

With $n$ a positive integer, evaluate the sum $$ \binom{n}{0} + 2 \binom{n}{1} + 2^2 \binom{n}{2} + \dots + 2^k \binom{n}{k} + \dots + 2^n \binom{n}{n} $$

I'm pretty sure that this has to do with the binomial theorem which states that $$ (a + b)^n = \sum_{k = 0}^n \binom{n}{k} a^{n-k}b^k $$ but I'm not sure how to apply it if that is indeed the case.