Exponential growth and Decay model:

If is a differentiable function of such that and for some constant , then .

is the initial value of and is the proportional constant.

Exponential growth occurs when , and exponential decay occurs when .

The initial quantity is .

The isotope has half life .

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When is and is .

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Substitute in .

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When , .

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When , .

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Amount after : .

Amount after : .