decays at a rate of 19% / year.

Question

A radioactive element decays at a rate of 19% / year. Initially, there is 10,000 lbs of this material. How much will be left after 21 years? (round to two decimal places)

A.7.14 lbs

B.About zero lbs

C.Solution not listed

D.119.73 lbs

Answer 1

After one year, the amount left is 10000 · (1 - 0.19).

After two years, the amount left is 10000 · (1 - 0.19)· (1 - 0.19).

And so after 21 years, the amount remaining is 10000 · (1 - 0.19)²¹.

Answer 2

Law of decay: m = m₀0.81^t. So after 21 years left m = m₀0.81²¹ = 10000·0.81²¹ = 119.73 lbs

So, right answer is D.

We get 0.81 = 1 - 0.19