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Exponential Decay

Concept

Exponential Decay

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,t, is time. y=abt y = a \cdot b^t Since the quantity decreases over time, the constant multiplier bb has to be less than 1.1. Thus, bb can be written as a subtraction of 11 and r,r, where rr is some positive number. The resulting function is called an exponential decay function.

The constant rr can then be interpreted as the rate of decay, in decimal form. A value of 0.12,0.12, for instance, would mean that the quantity decreases by 12%12\,\% over every unit of time. As for all other exponential functions, aa is the yy-coordinate of the yy-intercept. The base of the power, 1r,1 - r, is known as the decay factor, and since it is smaller than 11 the quantity decays towards 00 over time.