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