recurrence relations – How to solve $Tleft( nright) = 4Tleft({nover 2}right) + 2^{nover2}$ using Akra-Bazzi method?

$$Tleft( nright) = 4Tleft({nover 2}right) + 2^{nover2}$$

Let $g(n) = 2^{nover2}$, we can see that $|g'(n)|$ is not bounded by a polynomial. Therefore Akra-Bazzi method cannot be used to find bounds of the above problem. How come the above problem can still be solved using Master theorem which is just a corollary of Akra-Bazzi method.