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# Differential Equations - i hate worded questions! watch

1. I am absolutely flummoxed by this question. if anyone could just tell me the right representations i'm sure i could solve it, but i just don't understand the wording at all. [apologies, i'm no use with LaTeX]

"If you visit the mediaeval Great Hall, at the top of the high street in Winchester, just 20 minutes by car/train north of Southampton, you will see a circular table, 18 foot in diameter, that is claimed to be King Arthur's round table. If Arthur did really exist, it is most likely that he was a local chieftain in the dark ages with poor written records immediately following the Roman withdrawal in the 5th century AD." (which i'm pretty sure is all completely irrelevant)
"The table was recorded as having been in Winchester in 1484, but it was not known how old it really was. In 1976 the Council had it carbon-dated. The decay rate of Carbon-14 to Carbon-12 atoms is 1.245 x 10^-4 per year. The number of radioactive Carbon-14 atoms decayng was measured to be
dN/dt = -6.08
per minute per gramme. In living wood the decay rate is 6.68 particles per minute per gramme. Work out how old the table is and hence deduce whether this could be Arthur's round table?"

Thanks VERY much for any help
2. The rate given 1.245x10^-4 per year tells you that after one year 1-1.245x10^-4 of the original C14 remains.

That's 0.999875 or 99.9875%

Current level = original x 0.999875^years

Changing to base e

Current level = original x e^(-0.000125 * years)

Any use?
3. i think i see it now, thanks for your help. i had to manipulate your method slightly though.
4. (Original post by marcusmerehay)
i think i see it now, thanks for your help. i had to manipulate your method slightly though.
Great. Let us know how you get on will you? I'm interested. It was about time I learnt about carbon dating. (Should be able to do a maths question without that knowledge of course).

By the way can that negative value for dN/dt be correct?
5. i think that's more to do with the fact that it is decay.
6. (Original post by rnd)
Great. Let us know how you get on will you? I'm interested. It was about time I learnt about carbon dating. (Should be able to do a maths question without that knowledge of course).

By the way can that negative value for dN/dt be correct?
You usually put a negative infront to avoid a negative value.
7. The number of radioactive Carbon-14 atoms decaying was measured to be dN/dt = -6.08 per minute per gramme

In living wood the decay rate is 6.68 particles per minute per gramme.
Thanks. I was just puzzled that in the quote above one is negative and the other is positive.

btw how did you get all that negative rep? I've noticed a few of your posts and they seem ok to me. I guess you got it in other forums.

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