How to Build Exponential Models for Growth and Decay

Miacademy & MiaPrep Learning Channel

This video provides a clear, step-by-step tutorial on how to construct exponential function models for real-world scenarios involving growth and decay. The instructor, Randy, introduces a general template formula and demonstrates how to identify and substitute the correct values for initial quantity, growth/decay factors, and time intervals. The video specifically tackles the more complex concept of adjusting the exponent when the rate of change occurs over a specific time period (e.g., every 1.13 months or every 5,730 years), rather than just per single unit of time. The content explores two distinct examples in depth: a biological example involving a rabbit population to demonstrate exponential growth, and a scientific example involving Carbon-14 half-life to demonstrate exponential decay. Key themes include converting percentage increases and decreases into multiplication factors (e.g., 35% growth becomes a factor of 1.35) and understanding the logic behind fractional exponents in modeling time intervals. For educators, this video serves as an excellent instructional tool for Algebra 1 and Algebra 2 curriculums. It bridges the gap between basic exponential formulas and more sophisticated modeling required for advanced word problems. Teachers can use this to help students move beyond simple "plug and chug" methods by visualizing why the math works, specifically proving the validity of the equations by testing inputs like t=0 and the time interval itself.