A fragment of bone is discovered to contain 20% of the usual carbon-14 concentration. Estimate the age of the bone to the nearest hundred years, given that Carbon-1 is radioactive with half-life of 5730 years and the rate of decay is given by the following differential equation.

Question

dN/dt=-kN

N-# of undecayed atoms

Answer 1

dN/N = -k dt
log N = -kt
N = e^(-kt)

Now, we know that the fraction left after t years is

(1/2)^(-t/5730)

So just use the fact that 1/2 = e^-log2 and you can find k.

Answer 2

please post the answer