Problema Solution
An anthropologist finds bone that her instruments measure it as 0.146% of the amount of Carbon-14 the bones would have contained when the person was alive. How long ago did the person die?
The half life of carbon 14 is 5,730 years.
Answer provided by our tutors
We will use the formula:
A=A0*e^(kt) where
A is the amount at time t,
A0 is the initial amount, and
k is the decay constant unique to the substance
The half life of carbon 14 is 5,730 years means:
(1/2)A0 = A0*e^(k*5730)
A0*e^(k*5730) = (1/2)A0 divide both sides by A0
e^(k*5730) = 1/2
........
click here to see the solution of the equation for k
........
k = (1/5730) ln(1/2)
k = - 0.000120968094
Knowing that A = 0.00146A0 we need to find t:
A0*e^(kt) = 0.00146A0 divide both sides by A0
e^(-0.000120968094t) = 0.00146
........
click here to see the solution of the equation for t
........
t = 53,975.55 years
The person died 53,975.55 years ago.