TITLE: Why can't I find the moment $t_1$ where the radioactivity is gone?
QUESTION [0 upvotes]: Let's say $t_1$ is the moment the radioactivity is gone:
$A(t_1) = A_0 e^{-kt}$
$A(t_1) = 0$ since it's gone
But then what? How do I find $t_1$?
Since $A_0 e^{-kt} = 0$ then I can't "$\ln$" both of sides because there is no such thing as "$\ln(0)$"
So what do I do?

REPLY [2 votes]: That is because there is no finite $t_1$ such that $A(t_1)=0$. That is precisely what the math is telling you. $A(t)$ gets closer and closer to 0, but it never reaches it. It only approaches 0 asymptotically.
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