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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, $t,$ is time. $y = a \cdot b^t$ 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.