Since real time PCR was first developed, several approaches to estimating the initial quantity of template in an RT-PCR reaction have been tried. While initially only the early thermal cycles corresponding to exponential duplication were used, lately there has been an effort to use all of the cycles in a PCR. The efforts have included both fitting empirical sigmoid curves and more elaborate mechanistic models that explore the chemical reactions taking place during each cycle. The more elaborate mechanistic models require many more parameters than can be fit from a single amplification, while the empirical models provide little insight and are difficult to tailor to specific reactants.