anonymous
  • anonymous
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?
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
you know if \(t=9\) you have half of what you started with set \[e^{9k}=.5\] and solve for \(k\)
anonymous
  • anonymous
you got this? solve in two steps only
anonymous
  • anonymous
how do you solve for k?

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anonymous
  • anonymous
1) write in equivalent logarithmic form (take the log) 2) divide by 9
anonymous
  • anonymous
\[e^{9k}=.5\iff 9k=\ln(.5)\iff k=\frac{\ln(.5)}{9}\]
anonymous
  • anonymous
then if you want a decimal, use a calculator
anonymous
  • anonymous
i have no idea what that means haha. so is it: k= .1831?
anonymous
  • anonymous
no
anonymous
  • anonymous
wait is ln the button on the calculator for e?
anonymous
  • anonymous
http://www.wolframalpha.com/input/?i=ln%28.5%29%2F9 usually \(ln\) is the button and \(e\) requires the shift key
anonymous
  • anonymous
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
anonymous
  • anonymous
oh, the link helped. sorry we didn't learn this yet so I have no idea what im talking about
anonymous
  • anonymous
so the rate is k= -7.7 x 10 ^-2

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