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

Algebra ->  Exponential-and-logarithmic-functions -> 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      Log On


   

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(52812) About Me  (Show Source):
You can put this solution on YOUR website!
.

An equation of the radioactive decay in this case is 


    C%2A%281%2F2%29%5E%28t%2F5600%29 = 0.76%2AC,


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.


    %281%2F2%29%5E%28t%2F5600%29 = 0.76


Take logarithm base 2 from both sides


    -t/5600 = log%282%2C0.76%29


    -t/5600 = -0.39593


    t = 5600*0.39593 = 2217 years.      ANSWER