Half-Life? @CPhill

OK....we can solve this :

8  =  12* (1/2)^t/1620        where t is the time (in years) we are looking for

Divide both sides by  12

8/12  = (1/2)^t/1620

2/3  =  (1/2)^t/1620        take the log of both sides

log (2/3)  =  log(1/2)^t/1620          and we can write

log(2/3)  =  (t / 1620) * log (1/2)     divide both sides by log(1/2)

log (2/3) / log (1/2)  =  t  / 1620      multiply both sides by 1620

1620 * log (2/3) / log (1/2)  =  t   ≈  947.6  ≈   948  years

Thanks, Julius....look at the logic...if  t  =  1620, we have

A(1/2)^1620/1620  = 

A (1/2)¹  =

(1/2)A.........which is exactly what we would expect....1/2 of the amount, A, is what remains after 1620 years