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anonymous

  • 5 years ago

Is 1563 years the right answer? 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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    we start with the formula \[A=A_0(\frac{1}{2})^{\frac{t}{900}}\]

  2. anonymous
    • 5 years ago
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    that formula is because you know the half life is 900

  3. anonymous
    • 5 years ago
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    then whatever you started with you will have 70% = .7 of it when you are done so set \[.7=(\frac{1}{2})^{\frac{t}{900}}\] and solve for t

  4. anonymous
    • 5 years ago
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    take the log of both sides to get \[ln(.7)=\frac{t}{900} ln(.5)\]

  5. anonymous
    • 5 years ago
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    solve for t via \[t=\frac{900ln(.7)}{ln(.5)}\]

  6. anonymous
    • 5 years ago
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    i get 463 rounded but i could have made a mistake

  7. anonymous
    • 5 years ago
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    oh. that is an avail answer. i was way off..haha

  8. anonymous
    • 5 years ago
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    whew

  9. anonymous
    • 5 years ago
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    ok. thanks

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