Exponential growth and exponential decay are two of the most common applications of exponential functions. Systems that exhibit exponential growth follow a model of the form \(y=y_0e^{kt}\). In exponential growth, the rate of growth is proportional to the quantity present.Exponential Growth and Decay: Differential Equations 9.1 Observations about the exponential function In a previous chapter we made an observation about a special property of the function y = f(x) = ex namely, that dy dx = ex = y so that this function satisfies the relationship dy dx = y.

Example A revisited is Theorem 4.8 in the text. You may recognize the function (f t) as being basic exponential growth and decay, first encountered in Algebra II or Precalculus. Example B: The growth rate of a country’s population is proportional to its current population by a factor of 0.025. That is, P′(t)= 0.025 (P t).