The bones of a prehistoric man found in the desert of new Mexico contain approximately 5% of the original amount of carbon 14. If the half-life of carbon 14 is 5600 years, approximately how long ago did the man die?
Answers
Answer:
≈
8678.5
years ago
Explanation:
Quick note: The half life of C-14 is more commonly 5730 years, the value I will be using.
To find the age of an object with a radioactive element still present, we use this formula:
t
=
t
1
2
ln
(
N
t
N
0
)
−
ln
2
, where
t
is the age of the object,
t
1
2
is the half life of the element,
N
0
is the initial quantity of the element (usually 100),
N
t
is the remaining quantity of the element after time, and
ln
is the natural logarithm (base of
e
).
http://mathcentral.uregina.ca/beyond/articles/ExpDecay/Carbon14.html
As you can see, we have every value except for
t
. Plug our known variables into the equation, and we get
t
=
5730
ln
(
35
100
)
−
0.693
t
=
4011
log
2
−
0.693
t
≈
8678.5
Therefore the bones of the prehistoric man are roughly 8678.5 years old.
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