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.

100-0.0124=99.9876

10%=1/10

1/10P=P (0.999876) ^t

divide both sides by P

1/10=0.999876^t

take ln of both sides

ln (1/10) = t (ln (0.999876))

divide both sides by (ln (0.999876))

ln (1/10) / (ln (0.999876)) = t

use calculator

18568.08=t

about 18568 years