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anonymous

  • 5 years ago

A certain radioactive isotope has a half-life of approximately 900 years. How many years would be required for a given amount of this isotope to decay to 70% of that amount?

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  1. anonymous
    • 5 years ago
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    A=A0 e^rt

  2. anonymous
    • 5 years ago
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    1/2 = e^r(900)

  3. anonymous
    • 5 years ago
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    solve for r

  4. anonymous
    • 5 years ago
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    can you continue and show work

  5. anonymous
    • 5 years ago
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    \[e^{900r}=1/2\] 900 r ln e= ln 1/2 900 r= ln 1/2

  6. anonymous
    • 5 years ago
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    i have an idea

  7. anonymous
    • 5 years ago
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    write the formula as \[Q = Q_0(\frac{1}{2})^{\frac{t}{900}}\]

  8. anonymous
    • 5 years ago
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    set \[.7=(\frac{1}{2})^{\frac{t}{900}}\] and solve for t

  9. anonymous
    • 5 years ago
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    \[ln(.7)=\frac{t}{900}\times ln(\frac{1}{2})\]

  10. anonymous
    • 5 years ago
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    \[t=\frac{900ln(.7)}{ln(\frac{1}{2})}\]

  11. anonymous
    • 5 years ago
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    if you want to do it the first way using \[Q=Q_0e^{rt}\] then first you have to solve for r, then set the result equal to 1/2 and solve for t. it will work and you will get the same answer, but it is extra work

  12. anonymous
    • 5 years ago
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    ok. i see thank you

  13. anonymous
    • 5 years ago
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    imaram started the problem for you but you still have to solve for r, replace it in the equation, set = to 1/2 and then solve for t.

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