How long has the tree been dead?

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Homework Help Overview

The discussion revolves around determining the time since a tree has died based on the decay of a radioactive substance within it. The problem involves concepts of radioactive decay and the use of half-life in calculations.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the formula needed to relate the initial and final percentages of the radioactive substance, with one participant attempting to express the relationship in terms of an equation involving time.

Discussion Status

Some participants have expressed confidence in their understanding, while others have raised concerns about the validity of claims regarding having found the solution. There is an ongoing exploration of the correct formula and its components.

Contextual Notes

There is mention of uncertainty regarding the correct formula and the role of initial percentage p0 in the calculations. The discussion reflects a mix of confidence and skepticism about the answers provided.

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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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