This paper presents a new implementation of a 2-box absolute flow model, enabling the calculation of CO2 transfer between the atmosphere and a mixing reservoir representing the combined effect of the terrestrial and ocean regions. The model uses published values of anthropogenic CO2 fossil fuel emissions (CO2ff), atmospheric CO2 mixing ratio and nuclear weapons bomb yields, to compute atmospheric d13C and Δ14C time-series. The level of agreement between the calculated values and the accepted values for d13C is within ± 0.05 ‰, and for Δ14C is within ± 3‰, spanning 200 years. The model contains only seven internal parameters; these are varied to optimize the fit, leading to reasonable parameter values, indicating the validity of the method. In addition, the model shows how a rising CO2 exchange influx fluctuating with surface temperature is compatible with a nett atmospheric CO2 sink. The study demonstrates that a single CO2 residence time applies to both the 14C bomb pulse and the anthropogenic flux, contrary to the conventional view that "bomb radiocarbon and anthropogenic CO2 do not behave identically." [Joos 1994 Nature 370, 181–182]. It is shown that the difference in behaviour, claimed to be due to seawater chemistry, is not significant in practice since fluctuating bulk carbon dominates fluctuating isotopic ratio. A new analysis of the airborne fraction indicates that the assumption of a time-dependent exchange influx results in a similar residence time for bulk CO2 as for 14C in the nuclear bomb pulse, reinforcing the view that the 12C, 13C and 14C carbon isotopic forms of CO2 behave similarly in the carbon cycle.