The half-life of a certain radioactive substance is 5 years.What is the yearly percentage decay rate for this substance? Round your answer to two decimal places if necessary.
A) 10.65%
B) 12.94%
C) 13.87%
D) 10%

Question

The half-life of a certain radioactive substance is 5 years.What is the yearly percentage decay rate for this substance? Round your answer to two decimal places if necessary. ​
A) 10.65%
B) 12.94%
C) 13.87%
D) 10%

Quizplus · Accepted Answer

The yearly percentage decay rate can be found using the formula for half-life decay: $ P = 100(1 - 0.5^{1/t}) $, where $ P $ is the percentage decay rate and $ t $ is the half-life in years. Substituting $ t = 5 $ years, we get $ P = 100(1 - 0.5^{1/5}) \approx 13.86\% $, which rounds to 13.87%, making option C the correct choice. However, the correct explanation points towards option C, not B, as the correct answer due to a mistake in the initial choice selection. The accurate calculation aligns with option C, indicating a mistake in the initial response.

The Half-Life of a Certain Radioactive Substance Is 5 Years