Generally, when independent variable of a function is used as an exponent, the function is exponential. Hence, the following can be examples of exponential functions: , , or .Deriving functions of these types given the set of ordered pairs is difficult. This study was conducted to derive formulas for the arbitrary constants , and of the exponential function . It applied the inductive method by using definitions of functions to derive the arbitrary constants from the patterns produced. The findings of the study were: a) For linear, given the table of ordered pairs, equal differences in x produce equal first differences in y; b) for quadratic, given the table of ordered pairs, equal differences in x produce equal second differences in y; and c) for an exponential function, given a table of ordered pairs, equal differences in x produce a common ratio in the first differences in y. The study obtained the following forms: , , , Since most models developed used the concept of linear and multiple regressions, it is recommended that pattern analysis be used specifically when data are expressed in terms of ordered pairs.