The association of DNA methylation with age has been extensively studied. Previous work has investigated the trajectories of methylation with age, and developed predictive biomarkers of age. However, we still have a limited understanding of the functional form of methylation-age dynamics. To address this we present a theoretical framework to model the dynamics of DNA methylation at single sites. We show that this model leads to convergence to a steady-state methylation level at an exponential rate. By fitting the model to a dataset that measures changes in DNA methylation in the brain from birth to old age, we show that the timescales of this exponential convergence are heterogeneous across sites. To model this heterogeneity we generated a simulation of CpG Methylation changes with time and investigated the functional form of the dynamics of methylation with age under the empirical distribution of timescales estimated from the dataset. The resulting dynamics of the average methylation of the system were characterized and were found to closely follow an exponential trajectory. We conclude that DNA methylation can be modeled as a system that starts out of equilibrium at birth and approaches equilibrium with age in an exponential fashion. These insights illustrate the importance of accounting for nonlinear dynamics when utilizing age associated DNA methylation changes for constructing biomarkers of aging. Thus DNA methylation, along with the exponentially increasing risk of mortality with age, further establishes the exponential nature of aging.