Answer:
97,300 years
Step-by-step 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.
