If a tree dies and the trunk remains undisturbed for 13,261 years,what percentage of original is still present? (half-life of = 5730 years)
A)79.9%
B)20.1%
C)40.2%
D)30.2%
E)2.31%

Question

If a tree dies and the trunk remains undisturbed for 13,261 years,what percentage of original  is still present? (half-life of  = 5730 years)
A)79.9% 
B)20.1% 
C)40.2% 
D)30.2% 
E)2.31%

Quizplus · Accepted Answer

Since the half-life of the substance is 5730 years, we can find the number of half-lives that have occurred in 13261 years by dividing 13261 by 5730. This gives us approximately 2.314 half-lives. 
The percent of the substance remaining is calculated as (1/2)^(number of half-lives), giving us:
(1/2)^(2.314) ≈ 0.201
Therefore, approximately 20.1% of the original substance is still present after 13261 years. 
The correct answer is (B).

If a Tree Dies and the Trunk Remains Undisturbed for 13,261