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openstudyhelpplease

  • 2 years ago

A certain radioactive element decays according to N=No e ^-kt. If 50% of the original element sample remains after 9 days, what is the decay rate?

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  1. anonymous
    • 2 years ago
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    you know if \(t=9\) you have half of what you started with set \[e^{9k}=.5\] and solve for \(k\)

  2. anonymous
    • 2 years ago
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    you got this? solve in two steps only

  3. openstudyhelpplease
    • 2 years ago
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    how do you solve for k?

  4. anonymous
    • 2 years ago
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    1) write in equivalent logarithmic form (take the log) 2) divide by 9

  5. anonymous
    • 2 years ago
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    \[e^{9k}=.5\iff 9k=\ln(.5)\iff k=\frac{\ln(.5)}{9}\]

  6. anonymous
    • 2 years ago
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    then if you want a decimal, use a calculator

  7. openstudyhelpplease
    • 2 years ago
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    i have no idea what that means haha. so is it: k= .1831?

  8. anonymous
    • 2 years ago
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    no

  9. openstudyhelpplease
    • 2 years ago
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    wait is ln the button on the calculator for e?

  10. anonymous
    • 2 years ago
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    http://www.wolframalpha.com/input/?i=ln%28.5%29%2F9 usually \(ln\) is the button and \(e\) requires the shift key

  11. openstudyhelpplease
    • 2 years ago
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    ok, so i have to use the shift key right? i tried doing e ^.5 which was 1.64 and then divide that by 9 which was .1831

  12. openstudyhelpplease
    • 2 years ago
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    oh, the link helped. sorry we didn't learn this yet so I have no idea what im talking about

  13. openstudyhelpplease
    • 2 years ago
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    so the rate is k= -7.7 x 10 ^-2

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