A model of the ocean and seafloor carbon cycle is subjected to injection of new CO2 pulses of varying sizes to estimate the resident atmospheric fraction over the coming 100 kyr. The model is used to separate the processes of air-sea equilibrium, an ocean temperature feedback, CaCO3 compensation, and silicate weathering on the residual anthropogenic pCO2 in the atmosphere at 1, 10, and 100 kyr. The mean lifetime of anthropogenic CO2 is dominated by the long tail, resulting in a range of 30--35 kyr. The long lifetime of fossil fuel carbon release implies that the anthropogenic climate perturbation may have time to interact with ice sheets, methane clathrate deposits, and glacial/interglacial climate dynamics.