There was a sample of 800 milligrams of a radioactive substance to start a study.

Question

There was a sample of 800 milligrams of a radioactive substance to start a study. Since then, the sample has decayed by 5.3% each year. Let t be the number of years since the start of the study. Let y be the mass of the sample in milligrams. Write an exponential function showing the relationship between y and t.

Answer 1

After each year, the remaining mass is (1-0.053) = 0.947 times the mass at the start of the year. The exponential decay law is

y(t) = 800 (0.947)^t milligrams