## anonymous 5 years ago How old is a bone that has lost 25% of its carbon 14? (hint:the half life of Carbon 14 is is 5,770yrs)

1. anonymous

2374.4 yrs

2. anonymous

t = 1/k x ln[100/(100-25)] k = ln 2/ t(1/2)

3. anonymous

Are you sure? That's not one of the possible answers.

4. anonymous

Answeres can be: 21,106 yrs 2,390 yrs 3,120 yrs 5,770 yrs

5. anonymous

6. anonymous

2390.thats the closest

7. anonymous

approximations in the logarithms lead to deviations

8. anonymous

True. Thank you.

9. 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 $\frac{\ln(0.75)}{-0.0002013}=t \approx2394.75$

10. anonymous

yet another way is $.75=(\frac{1}{2})^\frac{t}{5700}$ $\frac{ln(.75)}{ln(.5)}=\frac{t}{5700}$ $t=5700\times \frac{ln(.75)}{ln(.5)}$