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27 March, 04:04

A scientist has a 120 mg sample of an unstable isotope. The amount of the substance remaining in the sample decreases at a rate of 16% each day. At the end of t days, there is less than 30 mg of the substance remaining. Which inequality represents this situation, and after how many days will the sample size remaining be less than 30 mg?

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  1. 27 March, 04:22
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    After each day there is 1 - 0.16 = 0.84 of the substance left

    The inequality is 120*0.84^t < 30

    120*0.84^t < 30

    0.84^t < 30/120 < 0.25

    t * ln 0.84 < ln 0.25

    t < ln 0.25 / ln 0.84

    t < 7.95

    Answer = 8 days
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