An effective Rosenblatt alternative for solvable groups

We prove the solvable analog to the effective Tits alternative.
Namely, let G be a finitely generated solvable group which is not virtually nilpotent. Then there is a constant m=m(G)>0 such that S^m contains two generators of a free semi-group, where S is an arbitrary generating set for G. In particular this implies uniform exponential growth for these groups.