Determination of the ¹⁴C content of dissolved inorganic carbon (DIC) is useful for dating of groundwater. However, in addition to radioactive decay, the ¹⁴C content in DIC (¹⁴C_DIC) can be affected by many geochemical and physical processes and numerous models have been proposed to refine radiocarbon ages of DIC in groundwater systems. Changes in the δ¹³C content of DIC (δ¹³C_DIC) often can be used to deduce the processes that affect the carbon isotopic composition of DIC and the ¹⁴C value during the chemical evolution of groundwater. This paper shows that a curved relationship of ¹⁴C_DIC vs. δ¹³C_DIC will be observed for groundwater systems if (1) the change in δ¹³C value in DIC is caused by a first-order or pseudo-first-order process, e.g. isotopic exchange between DIC and solid carbonate, (2) the reaction/process progresses with the ageing of the groundwater, i.e. with decay of ¹⁴C in DIC, and (3) the magnitude of the rate of change in δ¹³C of DIC is comparable with that of ¹⁴C decay. In this paper, we use a lumped parameter method to derive a model based on the curved relationship between ¹⁴C_DICand δ¹³C_DIC. The derived model, if used for isotopic exchange between DIC and solid carbonate, is identical to that derived by Gonfiantini and Zuppi (2003). The curved relationship of ¹⁴C_DIC vs. δ¹³C_DIC can be applied to interpret the age of the DIC in groundwater. Results of age calculations using the method discussed in this paper are compared with those obtained by using other methods that calculate the age of DIC based on adjusted initial radiocarbon values for individual samples. This paper shows that in addition to groundwater age interpretation, the lumped parameter method presented here also provides a useful tool for geochemical interpretations, e.g. estimation of apparent rates of geochemical reactions and revealing the complexity of the geochemical environment.