Cognitive Domain: Exponential And Logarithmic Functions In Mathematics

This chapter presents the exponential functions and their inverses the logarithmic equations. It is divided into four sections. The first section introduces the concept of percent change, an antecedent concept to the definition of exponential functions. The chapter avoids abstraction in favor of the presentation of the two main classes of functions in an applied setting. This approach is intended to build students’ intuition about the nature of exponential functions before attempting the more technically demanding tasks of writing and analyzing such functions. The topic of compound interest is partitioned into a separate short section. The next section covers logarithmic functions. This section does open with a more abstract presentation of topics. The initial abstraction is not offered for its own sake, however. Rather this abstraction is intended to simplify matters by reducing the amount of numerical calculation. This last section concludes with a return to exponential functions in applied settings and logarithms are used as tools for further analysis of these functions. Numerous examples and exercises are included throughout the chapter so that students can have ample opportunity for repetition to increase automated skills.