The Concept of Exponential Functions: A Student’s Perspective

Exponential functions represent an exceedingly rich and varied landscape for examining ways in which students construct their understandings of mathematical concepts. They are useful in modelling phenomena across many fields, including astronomy, economics, chemistry, biology and information theory, and are typically the mathematical “tool of choice” for exploring “bigness” and “smallness,” bringing these concepts into the range of human comprehension. They provide a dramatic contrast to linear functions in that the change they model is based on repeated multiplication instead of repeated addition; thus their rate of growth can be shocking.