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Exponential Growth and Decay

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Exponential Growth and Decay

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Exponential Growth and Decay

Exponential Growth and Decay

Exponential Growth and Decay

Exponential Growth and Decay

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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