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Thread: Natural decay question

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    Natural decay question

    twenty grams of salt is gradually dissolved in hot water. assume that the amount S left I dissolved after t minutes satisfies the law of natural decay dS/dt = -kS for some positive constant k.

    Show that S = 20e^-kt

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    Re: Natural decay question

    We may assume that if



    then



    for some constant .
    _______________________________________________

    Applying this to your question:



    and we know the initial amount of salt to be 20 grams, that is, . must then be equal to .

    Therefore, .

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