Calculate the amount, in grams, of an original 300-gram sample of radioactive isotope Potassium-40 remaining after 3.9 billion years if its half life equals 1.3 x 10^9 years.

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.