Problema Solution
In the formula a=Ie^kt, A is the amount of radioactive material remaining from an initial amount I at a given time t and k is a negative constant determined by the nature of the material. An artifact is discovered at a certain site. If it has 57% of the carbon-14 it originally contained, what is the approximate age of the artificial? (Carbon-14 decays at the rate of .0125% annually)
Answer provided by our tutors
Given:
k = -0.0125% which is -0.000125
A = 0.57*I
A/I = 0.57
By applying this,
A = I * e^(kt)
A/I = e^(kt)
0.57 = e^(-0.000125 *t)
ln(0.57) = ln(e^(-0.000125 *t))
ln(0.57) = -0.000125 *t
ln(0.57)/(-0.000125) = t
t = 4497 years approximately