Modeling Real-World Scenarios with Exponential Graphs

Miacademy & MiaPrep Learning Channel

This video lesson teaches students how to interpret and construct exponential function equations derived from graphs of real-world scenarios. It bridges the gap between abstract graphing concepts and practical applications by walking through three distinct examples: temperature cooling (exponential decay), botanical population growth (growth over specific time intervals), and financial investment appreciation (extrapolating future value). The narrator, Justin, guides viewers through the process of identifying initial values from y-intercepts and calculating growth or decay factors using identifiable points on the grid. The content focuses on the skill of reverse-engineering a function from visual data. Key themes include identifying the initial value (y-intercept), calculating growth/decay factors between points, adjusting exponents for different time intervals (e.g., growth every 2 years), and the concept of extrapolation. The video addresses the algebraic manipulation required to solve for base values and how to handle rational exponents when the growth period differs from the unit x-axis. For educators, this resource serves as an excellent direct instruction tool or review for Algebra students. It demonstrates not just the 'how' but the 'why' of exponential modeling, connecting mathematical functions to tangible changes in temperature, biology, and money. It is particularly useful for showing how to handle data points that are not sequential integers and introducing the concept of making predictions (extrapolation) based on established trends.