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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.
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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