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

Question

anonymous · Answer

2374.4 yrs

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

Answers*

anonymous · Answer

2390.thats the closest

anonymous · Answer

approximations in the logarithms lead to deviations

anonymous · Answer

True. Thank you.

anonymous · Answer

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 · Answer

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