SOLUTION: The​ half-life of​ carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows only 76​% of the​ carbon-14 expected in living​ matter, when did th

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Question 1143674: The​ half-life of​ carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows only
76​% of the​ carbon-14 expected in living​ matter, when did the tree​ die?
Answer by ikleyn(52832)   (Show Source): You can put this solution on YOUR website!
.

An equation of the radioactive decay in this case is 


     = ,


where C is the initial mass of carbon-14 in the sample; t is the time in years.


Simplify and solve for "t", which is the major unknown in this case.

Start canceling "C" in both sides.


     = 0.76


Take logarithm base 2 from both sides


    -t/5600 = 


    -t/5600 = -0.39593


    t = 5600*0.39593 = 2217 years.      ANSWER



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