Empirical studies suggest that the developmental plasticity of behavior often declines with age. We describe an unconstrained model of Bayesian behavioral development that addresses this phenomenon. This model is based on a few simple assumptions, e.g. that there are multiple possible values of the state of the world that animals are attempting to estimate, and that at birth or hatching, individuals may already have estimates of the state of the world, based on information provided to them by their ancestors. The model predicts that the effects of a given experience on a given behavior will virtually always decline with age, including situations in which individuals who express different levels of behavior early in life are sequentially exposed to different cues over the course of development.  Age-dependent declines in plasticity may be explained by the fact that exposure to even modestly reliable cues tends to reduce an individual's uncertainty about its estimate of the value of the state, and the more certain an individual is about its current estimate, the less that any subsequent experience will change that estimate. More generally, these results suggest that the real problem is not explaining why behavioral plasticity would decline with age, but explaining why it would not.