

All examples include systematic demonstration of Excel data manipulation and extensive graphing. It demonstrates a straightforward methodology for solving the key upper asymptotes for the proportionality equation using the Microsoft Excel via determining the "coefficient of determination". The article emphasizes the building of a straight-line proportionality relationship for the dose-response data in a log-linear and log-log graphs. Their difference is XY =, where Yu, Yb, Xu, and Xb are the upper and bottom asymptotes of Y and X variables.

The Alpha Beta (αβ) math is an extension of the XY math it emphasizes the association between the XY continuous nonlinear numbers and its associated asymptotes while the XY math is helpless in addressing the asymptotes relating to the nonlinear numbers. It introduces a new extended XY math (named Alpha Beta (αβ) math) concept for graphical expression of the experimental data, along with the presentation of simple mathematical equation having meaningful equation parameters. This article first reviews the fundamentals of nonlinear math followed by the analyses with examples. The data of pharmacokinetics and dose-response relationships in life science are nonlinear phenomena thus need to analyze from the viewpoint of nonlinear mathematics.
