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=(t_(1/2)ln(N_t/N_0))/-ln2, 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=(5730ln(35/100))/-0.693
t=((4011log)/2)/-0.693
t~~8678.5

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