Question 1059769
A= A0^e-0.0000284t 
A=(1/2)*Ao
Therefore 1/2Ao=Ao^e(-0.0000284t)
A0 cancel
take logs of both sides
log (1/2)=-0.0000284t, because ln of e^(t)=t.  Ln and e annihilate each other.
-0.693/-0.0000284=24,401 years=t
That compares favorably with quoted 25,000 years.