The statistical dynamics of population growth, wealth, and inequality are related through their common description as multiplicative stochastic processes. In these systems, variations in growth rates determine selection, relative wealth, and cooperation. Despite its relevance for biological and social sciences, we still lack a general theory that explains the dynamics of growth rates in terms of agent adaptation to their environment, heterogeneities of traits, and other behaviors. In this talk, we derive a general population dynamics of learning agents sharing and leveraging the knowledge of their environments to grow and reinvest their resources as individuals or groups. Growth rates emerge in the long-time limit as the mutual information between agents' signals and states of the environment and information synergies across signals. We show that, with knowledge of past and present conditions, sequential Bayesian inference becomes optimal for maximizing growth, formally associating growth rate dynamics with information dynamics. We discuss how this framework can address problems of inequality and cooperation in heterogeneous populations and lay the foundations for more robust interacting growth models