Determining Growth and Decay Rates in Exponential Functions

The Organic Chemistry Tutor

This instructional mathematics video provides a clear and methodical explanation of how to analyze exponential functions to determine their growth or decay characteristics. The video specifically focuses on the critical distinction between "growth/decay factors" (the base of the exponent) and "growth/decay rates" (the percentage of increase or decrease), a common point of confusion for algebra students. Through three distinct examples ranging from simple to complex, the narrator demonstrates how to calculate these values mathematically. The content covers key algebraic concepts including the general form of exponential functions, the relationship between the base value and the rate (b = 1 + r), and how to handle exponential functions where the exponent is a multiple of the variable (e.g., 3t). The video progresses from identifying simple rates to manipulating exponents to reveal the true underlying rate of change. This resource is highly valuable for Algebra 1, Algebra 2, and Pre-Calculus classrooms. It directly addresses standard curriculum requirements regarding exponential models and offers a step-by-step procedural guide that teachers can use to scaffold learning. The clear visual separation of "factor" and "rate" makes it an excellent tool for correcting misconceptions and helping students interpret the parameters of exponential equations in real-world contexts.