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Isotope half-life

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I am looking for the solution for this problem. Please show all assumptions, set up, and a detailed solution. I need set up, solving the equation and the final amount of material at any time.

A certain isotope has a half-life of 5 years. A sample of the isotope has...

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This is a problem regarding differential equations and half-life of an isotope.

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Although radioactive decay involves discrete events of nuclear disintegration, the number of events is so large that it can be treated like a continuum and the methods of calculus employed to predict the behavior. The result from the decay probability can be put in the differential form:

where = decay ...

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