How long has the tree been dead?

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SUMMARY

The discussion focuses on calculating the time since a tree has died based on the decay of a radioactive substance within it. The key formula derived is t = (tau) * ln(p0/p1) / ln(2), where p0 is the initial percentage of the substance, p1 is the percentage found in the fossilized remains, and tau is the half-life of the substance. The conversation highlights the importance of understanding exponential decay in this context. Participants confirm the correctness of the formula and its application in solving the problem.

PREREQUISITES
  • Understanding of radioactive decay and half-life concepts
  • Familiarity with natural logarithms and their properties
  • Basic algebra skills for manipulating equations
  • Knowledge of exponential functions and their applications
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  • Study the principles of radioactive decay and half-life calculations
  • Learn how to apply natural logarithms in various mathematical contexts
  • Explore exponential functions and their graphical representations
  • Investigate real-world applications of radioactive dating techniques
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Students in physics or environmental science, educators teaching concepts of decay, and researchers involved in dating organic materials will benefit from this discussion.

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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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