Generally, when the independent variable of a given exponential function is used as an exponent, the function is considered an exponential. Thus, the following can be examples of exponential functions: $f(x) = ab^x + c$, $f(x) = ae^bx + c$, or $f(x) = e^{a^2+bx+c}$. However, deriving functions of these types given the set of ordered pairs is difficult. This study was conducted to derive formulas for the arbitrary constants a ,b, and $c$ of the exponential function $f(x) = ab^x + c$. 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: $b=\sqrt[d]{r}$, $a=\frac{q}{b^n {(b^d-1)}}$, $c=p-ab^n$. 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.
Kemampuan Koneksi Matematik Siswa dalam Menyelesaikan Soal Investigasi Matematika
