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Exponential growth and exponential decay are both of the form

Q = Q_{0}e^{kt} |

where *Q*_{0} is the initial quantity, *t* is the time elapsed, and *k* is the rate constant.

*k* plays two roles. First, it determines whether the function will represent growth or
decay. If *k* is positive, then the function represents growth. If it is negative, then the
function represents decay.

Figure %: Exponential Growth (*k* positive) and Exponential Decay (*k* negative)

The second role that *k* plays is in setting the rate of growth or decay. The larger *k* is,
the faster the rate of change.

With exponential growth, the rate of increase goes up with time. This should be apparent from the derivative:

Q_{0}ke^{kt} |

Likewise, with exponential decay, the rate of decrease lessens with time.

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