We study exponential convergence of the minimal worst-case error, which means that converges to zero exponentially fast with increasing . Furthermore, we consider how the error depends on the dimension . To this end, we define the notions of weak, polynomial and strong polynomial tractability. In particular, polynomial tractability means that we need a polynomial number of information evaluations in and to compute an -approximation. We derive necessary and sufficient conditions on the sequences and for obtaining exponential error convergence, and also for obtaining the various notions of tractability. The results are the same for both classes . They are also constructive with the exception of one particular sub-case for which we provide a semi-constructive algorithm.