The authors explore the effects of a changing terrestrial biosphere on the atmospheric residence time of carbon dioxide using three simple ocean carbon cycling models and a model of global terrestrial carbon cycling. We find differences in model behavior associated with the assumption of an active terrestrial biosphere (forest regrowth) and significant differences if we assume a donor-dependent flux from the atmosphere to the terrestrial component (e.g., a hypothetical terrestrial fertilization flux). To avoid numerical difficulties associated with treating the atmospheric carbon dioxide decay (relaxation) curve as being well approximated by a weighted sum of exponential functions, we define the single half-life as the time it takes for a model atmosphere to relax from its present-day value half way to its equilibrium sub p CO2 value. This scenario-based approach also avoids the use of unit pulse (Dirac Delta) functions which can prove troublesome or unrealistic in the context of a terrestrial fertilization assumption.