In Years 9 and 10 of secondary schooling students are typically introduced to quadratic expressions and functions and related modelling, algebra, and graphing. This includes work on the expansion and factorisation of quadratic expressions (typically with integer values of coefficients), graphing quadratic functions, finding the roots of quadratic…

The study of the number of intersection points of y = a[superscript x] and y = log[subscript a]x can be an interesting topic to present in a single-variable calculus class. In this article, the authors present a classroom presentation outline involving the basic algebra and the elementary calculus of the exponential and logarithmic functions. The…

In this article, the authors consider the exponential curves y = ba[superscript x] where a, b [is a member of] R, a [greater than] 0, a [not equal to] 1, and b [not equal to] 1. The authors show that by fixing one of a or b the points (x[subscript 0],y[subscript 0) of tangency of y = ba[superscript x] and the line passing through the origin lie on…