How long will it take a given quantity of carbon-14 to lose 99.9% of its radioactivity if the half life is 5730 years? The formula I have been given is Q=ae^rt
This is using log and ln functions.
given:
when a = 2, Q=1 and t = 5730
so 1 = 2 e^(5730r)
0.5 = e^(5730r)
ln 0.5 = 5730r
r = ln 0.5/5730
so now we need:
.001 = e^((ln0/5/5730)t)
t(ln 0/5/5730) = ln 0.001
t = ln 0.001(5730)/ln 0/5 = 57103.9 years
or appr 57104 years