Chapter 4 Exponential and Logarithmic Functions

Exponential and logarithmic functions describe change governed by multiplication rather than constant addition. They arise in population growth, contaminant decay, compound processes, saturating systems, pH and other logarithmic measurements, and graphs spanning several orders of magnitude. This chapter follows the MATH 128 notes from exponential definitions and transformations through growth models, logarithmic functions, logarithm laws, equation solving, change of base, logarithmic scales, and flow-duration analysis. The emphasis is on translating among formulas, graphs, and practical interpretations while checking domain restrictions and units.

Learning outcomes. By the end of this chapter, you should be able to:

• graph and transform exponential and logarithmic functions;
• construct and interpret growth, decay, compound-interest, and logistic models;
• convert between exponential and logarithmic forms;
• expand and combine logarithmic expressions;
• solve exponential and logarithmic equations and reject invalid solutions;
• use the change-of-base formula and logarithmic scales; and
• interpret semi-log, log-log, and flow-duration graphs.