In this initial video, we will review the algebraic concept of direct proportionality and and apply it to the Law of Natural Growth. In so doing, we will derive the exponential growth model based on a differential equation, which assumes that the growth rate is directly proportional to the population. Duration: 6:54

The previous video used "Math" to solve the exponential growth model, and by "Math," we mean "Magic." This video will dispel that magic by taking you step-by-step through the solution to the differential equation y'=ky. Duration_17_30

Guest presenter and MIT graduate, Gordan Freeman explains to us how half-life is a major application of exponential decay, especially as it applies to headcrabs, xenomorphs, and the like. In Example 4, we apply Dr. Freeman's teachings to the fallout from the incident at Chernobyl. Hint: It's going to be around a while. Duration: 15:03

On Examples 5 and 6, use exponential growth and decay models to find the initial population of a batch of fruit flies and to discover how E.T. destroyed the video game industry in the 1980s. Duration: 13:47