Problema Solution
Carbon-14 is a radioactive substance with a half-life of approximately 5545 years and is frequently used to date archaeological findings. If an artifact discovered at a site has 58% of the carbon-14 that it originally contained, what is the approximate age of the artifact? Us the formula A=Ie^k^t where A is the amount at time t, I is the initial amount, and k is the decay constant unique to the substance.
Answer provided by our tutors
Let's plug the information given into the formula A = Ie^k^t
The half life is the time, T, that will give you a value of A(T) = 1/2 * I
We have T = 5545 years
A(T) = I * e^( k * T)
1/2 * I = I * e^( k * 5545)
e^(k * 5545) = 1/2
........
........
k = - 0.000125004
We need to find t, such that A(t) = 0.58I
0.58I = I * e^( - 0.000125004 *t)
e^(-0.000125004 * t) = 0.58
........
........
t = 4,357.68 years
The approximate age of the artifact is 4,357.68 years.