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HelpMe94

  • 2 years ago

What does the Exponential Decay Variables Mean? For Half Lifes Y=Ae^-bX

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  1. campbell_st
    • 2 years ago
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    ok so your formula is A is the initial population b is the decay coefficient X is normally the time. \[Y = Ae^{-bx}\] then then is the population half of the initial population of A for half life you will have \[\frac{Y}{A} = \frac{1}{2} \] so the equation becomes \[\frac{1}{2} = e^{-bX}\] you can find - bX by taking the log of both sides of the equation

  2. HelpMe94
    • 2 years ago
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    Another thing is if i know the half life in years = 5715 and the amount after 1000 years is 2 grams then what is the initial amount?

  3. HelpMe94
    • 2 years ago
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    so normal time is the amount of time passed?

  4. campbell_st
    • 2 years ago
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    so then X = 5715 this will help to find the decay constant - b \[\frac{1}{2} = e^{-b \times 5715}\] you'll need to solve for b by using logs... the when you have b you will be able to find A given Y = 2 and X = 1000

  5. campbell_st
    • 2 years ago
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    thats correct.

  6. HelpMe94
    • 2 years ago
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    ok so is 1/2 the grams?

  7. HelpMe94
    • 2 years ago
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    also if it is then why is it divided by 1

  8. campbell_st
    • 2 years ago
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    well half life means you end up with 1/2 of what you start with... and because you are given X = 5715 you can calculate b

  9. HelpMe94
    • 2 years ago
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    give me a moment...

  10. campbell_st
    • 2 years ago
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    the calculation is \[\ln(\frac{1}{2}) = -b \times 5715\]

  11. HelpMe94
    • 2 years ago
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    i see that but what i don't understand is the 1/2

  12. campbell_st
    • 2 years ago
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    half life if you start with 100 gm then 50gm is the half life, 20gm then 10gm is the half life. 3 gm then 1.5 gm is the half life. so its when the initial quantity gets to half its size.

  13. campbell_st
    • 2 years ago
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    so if you really don't need to know the initial quantity if you know how long it takes to get 1/2 life...

  14. HelpMe94
    • 2 years ago
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    oh so is 1/2 just to solve to get b then plug in to the equation for the 1000 years =x to get the answer...

  15. campbell_st
    • 2 years ago
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    thats it... b will be a positive decimal...

  16. HelpMe94
    • 2 years ago
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    ok let me see if this checks out for a second

  17. HelpMe94
    • 2 years ago
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    one thing were did A go?

  18. HelpMe94
    • 2 years ago
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    oh wait i see

  19. HelpMe94
    • 2 years ago
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    y/a is 1/2

  20. campbell_st
    • 2 years ago
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    the ratio of Y/A = 1/2

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