Using Logarithmic Models to Solve Real-World Problems

Miacademy & MiaPrep Learning Channel

This video provides a practical demonstration of how to apply logarithmic and exponential models to solve real-world word problems. Using a specific example involving the shrinking area of a region in the Amazon jungle, the presenter, Randy, guides viewers through analyzing an exponential decay formula ($A = 2816 \cdot 10^{-0.1t}$). The video breaks down how to identify variables, determine initial conditions, and answer two distinct types of questions: solving for a future value given time, and solving for time given a specific value. The content focuses heavily on the algebraic mechanics required to solve these problems. Key topics include identifying knowns and unknowns, isolating the exponential term in an equation, converting exponential equations into logarithmic form to solve for a variable in the exponent, and calculator syntax tips (specifically distinguishing between the negative sign and subtraction key). It contrasts the ease of solving for the dependent variable (Area) versus the more complex steps required to solve for the independent variable (Time). For educators, this video serves as an excellent bridge between abstract algebraic skills and applied mathematics. It validates the question "when will we use this?" by applying logarithms to environmental science. The step-by-step framework presented at the end—Identify Variables, Write Equation, Solve—provides students with a transferable strategy for tackling any modeling word problem in Algebra II or Pre-Calculus contexts.