anonymous
  • anonymous
How old is a bone that has lost 25% of its carbon 14? (hint:the half life of Carbon 14 is is 5,770yrs)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
2374.4 yrs
anonymous
  • anonymous
t = 1/k x ln[100/(100-25)] k = ln 2/ t(1/2)
anonymous
  • anonymous
Are you sure? That's not one of the possible answers.

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anonymous
  • anonymous
Answeres can be: 21,106 yrs 2,390 yrs 3,120 yrs 5,770 yrs
anonymous
  • anonymous
Answers*
anonymous
  • anonymous
2390.thats the closest
anonymous
  • anonymous
approximations in the logarithms lead to deviations
anonymous
  • anonymous
True. Thank you.
anonymous
  • anonymous
Another way is: \[A=A_0e^{rt}\] Work out what the rate of change is, in other words r for the C14 \[1/2 = e^{r5770}\] take ln of both sides \[\ln(1/2)=r\times5770\] \[r=\frac{\ln(1/2)}{5770} \approx 0.00012013\] substitute that back into the equatio nfor 25% gives \[0.75 = e^{-0.00012013t}\] finally \[\frac{\ln(0.75)}{-0.0002013}=t \approx2394.75\]
anonymous
  • anonymous
yet another way is \[.75=(\frac{1}{2})^\frac{t}{5700}\] \[\frac{ln(.75)}{ln(.5)}=\frac{t}{5700}\] \[t=5700\times \frac{ln(.75)}{ln(.5)}\]

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