Question

Carbon-14 decays at a constant rate, so it can be used to determine the age of fossils. In particular, if the original amount of Carbon-14 present is A0, then A(t) = A0e^(-kt) can be used find the amount of amount of Carbon-14 remaining after t years. Given that the half-life of Carbon-14 is 5,730 years, what is the value of the decay constant k to 5 decimal places?
-_____ k
_____ A0 = A0e
k ~= ______

Answer 1

In this scenario we know that carbon14 at a given time A(t) = A0e^(-kt), where A0 is the original carbon present, t is time in years and k is the constant.

As we are working with the half life of carbon being 5730 years, we assume original carbon-14 content, A0 = 1, and carbon-14 at half life 5730 years, A(t) = 0.5.

i.e. 
0.5 = 1e^(-5730k)
apply Ln to both sides of equation to cancel e
ln(0.5) = -5730k
k = ln(0.5) / -5730
k = -0.69315 / - 5730 = 1.20968 x 10^-4