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19 June, 17:32

A certain radioactive compound decays at a rate of 0.0345% per year. Given 200 grams of the compound, how much will remain after 500 years? After 5000 years? How about 500 years ago?

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  1. 19 June, 19:01
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    After 500 years = 165.5 grams

    After 5000 years = 0 grams

    500 years ago = 234.5g grams

    Step-by-step explanation:

    This radioactive compound decays at 0.0345% per year

    For 200 grams of the compound it decays at a rate of 0.0345% per year

    0.0345% of 200 = 345 / 100,000 * 200

    = 0.069

    So, for every year, 0.069 grams of this compound decays

    In 500 years, (0.069 * 500) of this compound will decay

    This gives 34. 5 grams

    Therefore, Th amount which will remain after 500 years is;

    200 - 34. 5 = 165.5 grams

    After 5000 years,

    200 - (0.069 * 5000) will remain

    = 200 - (345)

    = - 145

    Since the value is negative, it means that all of the compound would have decayed after 5000 years so, there will be nothing left = 0 grams

    The amount of the compound 500 years ago will be;

    200 + (0.069 * 500)

    = 200 + (34.5)

    = 234.5g grams
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