The carbon cycle describes the transformations of carbon as it cycles through living organisms and the physical environment. A key step in the cycle is the return of carbon dioxide to the atmosphere via microbial consumption of organic carbon. Observations show that the rate of consumption of organic matter slows down like the inverse of its age. These observations are consistent with predictions of a simple reaction-diffusion model. More generally, the observed aging effect results from the decay of any mixture composed of a wide range of decay rates. Its occurence in the carbon cycle may also extend to inorganic processes as well.