anonymous
  • anonymous
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.
Mathematics
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anonymous
  • anonymous
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.
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
we start with the formula \[A=A_0(\frac{1}{2})^{\frac{t}{900}}\]
anonymous
  • anonymous
that formula is because you know the half life is 900
anonymous
  • anonymous
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

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anonymous
  • anonymous
take the log of both sides to get \[ln(.7)=\frac{t}{900} ln(.5)\]
anonymous
  • anonymous
solve for t via \[t=\frac{900ln(.7)}{ln(.5)}\]
anonymous
  • anonymous
i get 463 rounded but i could have made a mistake
anonymous
  • anonymous
oh. that is an avail answer. i was way off..haha
anonymous
  • anonymous
whew
anonymous
  • anonymous
ok. thanks

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