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23 January, 16:15

an element with a mass of 540 grams decays by 17.9% per minute to the nearest tenth of a minute how long will it be until there are 90 grams of the element remainibg

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  1. 23 January, 16:47
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    It'll take approximately 9.1 minutes

    Step-by-step explanation:

    The decay of this element can be modeled by the following expression:

    m (t) = 540 * (1 - 0.179) ^t

    Where m is the mass of the element in a given minute t. This expression comes from a compounded interest formula, with negative rate, since they will work in the same manner. Therefore to find how long until it reaches 90 g, we need to make m = 90 and solve for t.

    90 = 540 * (0.821) ^t

    (0.821) ^t = 90 / 540

    (0.821) ^t = 1/6

    ln (0.821^t) = ln (1/6)

    t*ln (0.821) = ln (1) - ln (6)

    t*ln (0.821) = - ln (6)

    t = - ln (6) / ln (0.821) = 9.08452

    It'll take approximately 9.1 minutes
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