Comparing Linear vs. Exponential Growth: Which Wins?

Miacademy & MiaPrep Learning Channel

This video provides a clear, step-by-step comparison between linear and exponential functions using real-world financial scenarios. It begins with a classic "lottery dilemma"—choosing between a large daily lump sum (linear) or a penny that doubles daily (exponential)—to illustrate the explosive nature of exponential growth. The narrator, Justin, uses graphs to visually demonstrate how exponential functions, despite often starting with smaller values, eventually surpass linear functions due to their compounding nature. The video progresses to more complex scenarios, such as comparing two savings accounts with different terms to determine which is more profitable over a specific time frame. It introduces the critical concept that while exponential growth always wins eventually, it may not be the better choice in the short term. The final segment dives into advanced comparisons between different exponential functions, teaching students how to identify true growth factors even when exponents are manipulated (e.g., converting a fractional exponent into a standard growth rate). For educators, this video is an excellent tool for Algebra 1 and 2 curriculums. It bridges the gap between abstract equations and tangible outcomes using money, a topic that naturally engages students. The visual graphing sequences effectively scaffold the concept of "rate of change" and provide opportunities for students to predict, calculate, and analyze functional behavior before seeing the solution.