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teller

  • one year ago

Can someone please help me ? The half-life of a radioactive isotope is the time it takes for a quantity of the isotope to be reduced to half its initial mass. Starting with 165 grams of a radioactive isotope, how much will be left after 3 half-lives?Use the calculator provided and round your answer to the nearest gram.

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  1. anonymous
    • one year ago
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    \[A=A_0\cdot \left( \frac{ 1 }{ 2 } \right)^k\]where \(A_0\) is the initial amount \(A\) is the amount remaining after k half-lives and k is the number of half-lives

  2. teller
    • one year ago
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    So 165=3*(1/2)^k?

  3. anonymous
    • one year ago
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    no... A = 165*(1/2)^3

  4. teller
    • one year ago
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    165/8?

  5. anonymous
    • one year ago
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    yep

  6. teller
    • one year ago
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    but it has to be rounded to the nearest gram how do I do that? It can't be in fraction form.

  7. anonymous
    • one year ago
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    divide and see what you get... the problem says to use the calculator provided but any calculator will work... or you can use long division

  8. teller
    • one year ago
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    divide it by what do I divide 165 by 8?

  9. anonymous
    • one year ago
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    yes, that is another way to represent 165/8

  10. teller
    • one year ago
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    I got 20.625 is that right?

  11. anonymous
    • one year ago
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    does that make sense to you? what is 20 * 8?

  12. teller
    • one year ago
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    160

  13. anonymous
    • one year ago
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    so let's rewrite: \[\frac{ 20\cdot 8 }{ 8}+\frac{ 5 }{ 8 }=\frac{ 160 }{ 8 }+\frac{ 5 }{ 8 }=\frac{ 165 }{8}\]and 5/8 is less than 1 but more than 1/2 = .5, correct?

  14. anonymous
    • one year ago
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    so final answer, rounded to the nearest gram?

  15. teller
    • one year ago
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    I'm confused at what I'm supposed to be rounding...

  16. anonymous
    • one year ago
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    20.625

  17. teller
    • one year ago
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    But how do I do that I already did that and I gave you the answer but you never told me if it was right.

  18. teller
    • one year ago
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    I got that but how do I round that?

  19. anonymous
    • one year ago
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    20.625 is not rounded to the nearest gram... 20.625 grams is the exact answer but they want the answer rounded to the nearest gram. which is closer to 20.625... 20 or 21?

  20. teller
    • one year ago
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    20

  21. teller
    • one year ago
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    no wait 21

  22. anonymous
    • one year ago
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    there you go!

  23. teller
    • one year ago
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    so 20.621?

  24. anonymous
    • one year ago
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    ?

  25. teller
    • one year ago
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    you said 21 so 20.621

  26. anonymous
    • one year ago
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    no... to the nearest gram... no numbers after the decimal!!!

  27. teller
    • one year ago
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    oh okay thank you

  28. teller
    • one year ago
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    Mind helping me with another one?

  29. anonymous
    • one year ago
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    i would but i'm heading out. going for a bike ride. good luck!

  30. teller
    • one year ago
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    Alright thanks

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