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22 November, 04:45

The function f (x) = 500 (0.5) ^x/100 models the amount of pounds of a particular radioactive material stored in a concrete vault, where x is the number of years since material was put into the vault. Find the amount of radioactive material in the vault after 140 years. Round to the nearest whole number.

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  1. 22 November, 04:52
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    the amount of radioactive material in the vault after 140 years is 190 pounds.

    Step-by-step explanation:

    The given model for the amount of pounds of a particular radioactive material is

    f (x) = 500 (0.5) ^ (x/100)

    where

    x is the number of years since the material was put into the vault f (x) is the amount of pounds of the material

    Therefore, the amount of radioactive material in the vault after 140 years will be

    f (140) = 500 (0.5) ^ (140/100)

    f (140) = 189.5 pounds

    This answer rounded off to the nearest whole number will be

    f (140) = 190 pounds

    Therefore, the amount of radioactive material in the vault after 140 years is 190 pounds.
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