Question

Living organisms can be dated by the amount of carbon-14 present at time(t)

compared to the amount present when the organism was alive. The half-life of carbon-14 is 5730. How long would it take for a 185 microgram sample of carbon-14 decay to 24 grams? (Round to the nearest 100 years.)​

Answer 1

97,300 years

Explanation:

The decay formula is ...

decayed value = (initial value)×(1/2)^(t/(half-life))

Filling in the numbers and solving for t, we get ...

185×10^-6 = 24×(1/2)^(t/5730)

Taking logs, we have ...

log(185×10^-6) = log(24) + (t/5730)log(1/2)

(log(185×10^-6) -log(24))×5730/log(1/2) = t . . . . . solve for t

(-3.73283 -1.38021)×5730/-0.301030 = t = 97324.9 ≈ 97,300

It would take about 97,300 years for 24 grams to decay to 185 micrograms.