How long has the tree been dead?

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To determine how long a tree has been dead based on the decay of a radioactive substance, the relevant formula is t = (tau) * ln(p0/p1) / ln(2), where p0 is the initial percentage of the substance and p1 is the percentage found in the fossilized remains. The discussion highlights confusion about the correct formula for calculating time since death, with initial attempts focusing on decay equations. A participant confirms the correct formula after some back-and-forth, emphasizing the importance of clarity in problem-solving. The conversation underscores the need for precise mathematical expressions in decay problems. Understanding these concepts is essential for accurate scientific analysis.
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Homework Statement


A tree contains a known percentage p0 of a radioactive substance with half-life tau. When the tree dies the substance decays and isn't replaced. If the percentage of the substance in the fossilized remains of such a tree is found to be p1, how long has the tree been dead?

Homework Equations


I don't know what formula to use but I know that I have to solve for t in the formula. So I just need to know the formula.

The Attempt at a Solution


p1=(1/2)^(-t/tau)
This is all I can come up at this moment. I don't know if this is the right formula.
 
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You can use a positive exponent with (1/2) as your base or you can use a negative exponent with 2 as the base. And p0 should be in there somewhere.
 
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I got it! Thanks for the help!
 
Math10 said:
I got it! Thanks for the help!

If you have got it why not tell us the answer? The last poster who told me they'd got it, when I asked, hadn't, and I think this is true of quite a lot who say that.
 
The answer is (tau)*ln(p0/p1)/ln(2).
 
Right
 

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