Fundamental to the efficacy of cognitive training (CT) is its dose. Here we used the power and breadth afforded by a large dataset to measure precisely dose-response (D-R) functions for CT and to examine the generality of their magnitude and form. The present observational study involved 107,000 users of Lumosity, a commercial program comprising computer games designed to provide CT over the internet. In addition to training with Lumosity games, these users took an online battery of cognitive assessments (NeuroCognitive Performance Test, NCPT) on two or more occasions separated by at least 10 weeks. Changes in performance on the NCPT between the first and second assessments were examined as a function of the amount of intervening gameplay. The resulting D-R functions were obtained both for overall performance on the NCPT and performance on its eight subtests. Also examined were differences between D-R functions from demographic groups defined by age, gender, and education. Monotonically increasing D-R functions, well fit by an exponential approach to an asymptote, were found consistently for overall performance on the NCPT, performance on seven of the eight subtests, and at each level of age, education, and gender. By examining how individual parameters of the D-R functions varied across subtests and groups, it was possible to measure separately changes in the effects on NCPT performance of 1) transfer from CT and 2) direct practice due to repeated testing. The impact of both transfer and direct practice varied across subtests. In contrast, while the effects of direct practice diminished with age, those of transfer remained constant. Besides its implications for CT by older adults, this latter finding suggests that direct practice and transfer do not involve identical learning processes, with transfer being limited to learning processes that remain constant across the adult lifespan.