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Answer:
The current amount of the Potassium-40 sample is approximately 37.521 grams.
Explanation:
The amount of the sample of the radioactive isotope decays exponentially in time, the amount of mass of the sample as a function of time (), in grams, is described below:
(1)
Where:
- Initial mass, in grams.
- Time, in years.
- Time constant, in years.
The time constant can be found from half life (), in years, described in statement:
(2)
If we know that ,
and
, then the current amount of the sample is:
The current amount of the Potassium-40 sample is approximately 37.521 grams.