Question

Carbon–14 is a radioactive isotope that decays exponentially at a rate of 0.0124 percent a year. How many years will it take for carbon–14 to decay to 10 percent of its original amount? The equation for exponential decay is At = A0e–rt.

Answer 1

A(t) = Ao*e^(-rt)

-rt = ln [ A(t)/ Ao]

t = - ln [ A(t)/ Ao] / r

r= 0.0124% = 0.0124/100 = 0.000124

A(t)/A0 = 10% = 10/100 = 0.1

Now substitute

t = - ln [0.1] / 0.000124 = 2.3025851 / 0.000124 = 18,569 years

Your result will depend on how you round ln(0.1).