A hallmark of the adaptive immune response is the proliferation of pathogen-specific lymphocytes that leave in their wake a long lived population of cells that provide lasting immunity. A subject of debate is at which time point post infection those memory cells are produced during an adaptive immune response. In two ground-breaking studies, [Buchholz et al., 2013] and [Gerlach et al., 2013] introduced a new experimental method that allowed them to determine the number offspring from individual lymphocytes in vivo at a single harvesting time point. Through the development, application and fitting of a mathematical model, the authors of [Buchholz et al., 2013] concluded that memory cell precursors are produced before the effector cells that clear the original pathogen, contrary to prior understanding. Cohort level cell data in the paper [Kinjyo et al., 2015], however, challenges that deduction. In this thesis we sought to quantitatively reconcile these two reports by adopting the mathematical methodology of [Buchholz et al., 2013] to make it suitable for drawing inferences from the data in [Badovinac et al., 2007], [Schlub et al., 2010] and [Kinjyo et al., 2015]. When fitting to spleen and blood data reported in these papers, under the assumptions of the model, our conclusion is consistent with [Buchholz et al., 2013]: memory precursor cells appear before effector cells. However, an alternative possibility supported by the data in [Kinjyo et al., 2015] is that memory is created after the expansion phase, a deduction not possible from the data or mathematical methods in [Buchholz et al., 2013].