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?

1 Answer
Sep 25, 2017

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=t12ln(NtN0)ln2, where t is the age of the object, t12 is the half life of the element, N0 is the initial quantity of the element (usually 100), Nt 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=5730ln(35100)0.693
t=4011log20.693
t8678.5

Therefore the bones of the prehistoric man are roughly 8678.5 years old.