We include learning in a standard equilibrium business cycle model with explicit growth. We use the model to study how the economy's agents could learn in real time about the important trend-changing events of the postwar era in the U.S., such as the productivity slowdown, increased labor force participation by women, and the "new economy" of the 1990s. We find that a large fraction of the observed variance of output relative to trend can be attributed to structural change in our model. However, we also find that the addition of learning and occasional structural breaks to the standard and widely-used growth model results in a balanced growth puzzle, as our approach cannot completely account for observed trends in U.S. aggregate consumption and investment. Finally, we argue that a model-consistent detrending approach, such as the one we suggest here, is necessary if the goal is to obtain an accurate assessment of an equilibrium business cycle model.