Why do epidemics and investments share the same mathematical DNA?
In short: From viral outbreaks to compound interest, many systems follow a predictable pattern of rapid expansion. This video explains the calculus behind these trends by introducing separable differential equations.
The core reason for exponential growth in diverse fields is that the rate of change is proportional to the current size. In mathematics, this is expressed as the ordinary differential equation y'=ky. Because the growth depends on how much of 'y' already exists—whether it is infected people or dollars in an account—the solution naturally results in an exponential curve.
Dr. Trefor Bazett demonstrates how to solve these types of problems using a method called separation of variables. This technique provides a general procedure for solving separable equations, which serve as fundamental models for understanding early-stage epidemic dynamics and continuous compounding.
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- Summary by Intellect · source: Why Exponential Growth?? Intro to Separable Differential Equations
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