This paper presents an approach to the problem of estimating the number of exponential functions and the pertinent parameters in the output of a radioactive tracer kinetic process. In particular, application of a criterion called an information theoretical criterion (AIC) for the estimation of the number of exponential functions is proposed; AIC was introduced by Akaike for the estimation of the order of linear dynamical systems and has been successfully applied for statistical model identification in a wide range of fields. Also, the maximum likelihood method was applied in order to evaluate AIC and to estimate decay constants and coefficients.