To thrive in diverse environments, cells must represent extracellular change intracellularly despite stochastic biochemistry. We introduce a quantitative framework for investigating the organization of information within a cell. Combining single-cell measurements of intracellular dynamics with a new, scalable methodology for estimating mutual information between time-series and a discrete input, we demonstrate that extracellular information is encoded in the dynamics of activation of transcription factors and that information is lost with alternative static statistics. We screened the activation of 10 transcription factors in budding yeast across 13 environmental transitions. Each transcription factor reports differently, and it is only their collective response that distinguishes between multiple environmental states. Changes in the activation dynamics of transcription factors thus constitute a precise, distributed internal representation of extracellular change, and we predict that such multi-dimensional representations are common in cellular decision-making. The framework presented in this work will be applicable to investigate information encoding in any dynamic system such as stress responses, cell differentiation, and programmable synthetic circuits.