Several mathematical equations for describing the growth curve of modern and fossil carbonate samples are discussed. The best approximation for the dose response of the g = 2.0006 ESR dating signal in aragonitic coral and shell samples was found by a combination of three single exponential saturation functions. Also the isothermal decay curves of the ESR signal proved to be best fitted by the combination of three first order decay functions. The lifetimes of the three components were obtained from an Arrhenius plot. For different species of mollusc shells the lifetime of the less stable component was found in the range 30-90 ka at 2-degrees-C. It can be removed by heating the samples at 180-degrees-C for a period of 2 h.