SOLUTION: The​ half-life of​ carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows only 73​% of the​ carbon-14 expected in living​
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Question 1088726: The half-life of carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows only 73% of the carbon-14 expected in living matter, when did the tree die?
The tree died about ______ years ago?
(Do not round until the final answer. Then round to the nearest whole number.)
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
formula is:
where:
= future amount
= present amount
= constant of proportion.
= time
half life of carbon is given by the equation:
because:
half life of carbon is years.
solve for and then you can solve the problem.
take log of both sides of equation of to get:
this becomes:
divide both sides of this equation by to get:
solve for to get:
which becomes:
if the tree has only %= of the carbon left, then your equation of:
becomes:
which becomes:
take the log of both sides of this equation to get:
which becomes:
divide both sides of this equation by to get:
solve for to get:
years
Then round to the nearest whole number: years
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