SOLUTION: A certain element has a half life of 1.5 billion years. a. You find a rock containing a mixture of the element and lead. You determine that 45​% of the original element&#82

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Question 1119681: A certain element has a half life of 1.5 billion years.
a. You find a rock containing a mixture of the element and lead. You determine that 45​% of the original element​ remains; the other 55​% decayed into lead. How old is the​ rock?
b. Analysis of another rock shows that it contains 20​% of its original​ element; the other 80​% decayed into lead. How old is the​ rock?
Answer by greenestamps(13195) About Me  (Show Source):
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The fraction of the original amount remaining after n half-lives is %281%2F2%29%5En.

So for the first question you need to solve
%281%2F2%29%5En+=+0.45

and for the second you need to solve
%281%2F2%29%5En+=+0.20

Using logarithms or a graphing calculator, the solution in the first case is n=1.152, making the age of the rock (1.152)(1.5) = 1.728 billion years; the solution in the second case is n = 2.322, making the age of the rock (2.322)(1.5) = 3.483 billion years.