Exponential decay is when a quantity decreases by the same factor over equal intervals of time. This leads to an exponential function, where the independent variable in the exponent, t, is time. y=a⋅bt Since the quantity decreases over time, the constant multiplier b has to be less than 1. Thus, b can be written as a subtraction of 1 and r, where r is some positive number. The resulting function is called an exponential decay function.
The constant r can then be interpreted as the rate of decay, in decimal form. A value of 0.12, for instance, would mean that the quantity decreases by 12% over every unit of time. As for all other exponential functions, a is the y-coordinate of the y-intercept. The base of the power, 1−r, is known as the decay factor, and since it is smaller than 1 the quantity decays towards 0 over time.