We start with the basic exponential growth and decay models. Khan Academy is a 501c3 nonprofit organization. To describe these numbers we often use orders of magnitude.
As with exponential growth there is a differential equation associated with exponential decay.
It occurs when the instantaneous rate of change that is the derivative of a quantity with respect to time is proportional to the quantity itself. In this function a represents the starting value such as the starting population or the starting. It occurs when the instantaneous rate of change that is the derivative of a quantity with respect to time is proportional to the quantity itself. The exponent in the equation for decay is a fraction that is between 0 and 1.