Carbon dioxide does not have a mean residence time in the atmosphere as there are a range of processes that exchange carbon dioxide between the atmosphere and other carbon reservoirs, operating on a wide range of time-scales. An indication of residence time can be seen from experiments using the Met Office Hadley Centre's Earth system model, HadGEM2-ES, in which for the current climate, the fraction of a pulse of carbon dioxide remaining in the modelled atmosphere after 20 and 100 years is 62% and 45% respectively1. This compares closely with other models used in the experiments in the paper referenced.
1 Joos et al. 2013, Carbon dioxide and climate impulse response functions for the computation of greenhouse gas metrics: a multi-model analysis. Atmos. Chem. Phys., 13, 2793-2825. doi:10.5194/acp-I 3-2793-2013.