How can we determine the age of ancient substances using radiocarbon dating?

[dumbadum]

I was doing a question which gave the decay rate of the ancient substance as 13.2dpm. The question asked that assuming living plants now has a disintegration rate of 15.3 dpm, and the half-life of carbon-14 is 5730 years, what is the age of the ancient substance.

I went on the internet, and got a question similar to this:
Charcoal @ stone Henge has C14 in concentration which produced 8.2dpm/gram
normal C14 from a tree is 13.5 dpm/g
half life of C14 is 5568 years,
what is the age of the charcoal.
There was a solution on the website which went something like this:

Law of radioactive decay:
Radioactive decay at rate that is proportional to the amount of radioactive material present.

d/dt (decay(t)) = -kdecay(t)
t=0 at the time when stone henge is built
decay(0) = 13.5
decay(t) = 13.5 x 10^(-kt)
13.5x10^(-k5568)=0.5(13.5)
Then I just got so confused...
Please explain how exactly to start a question regarding radioactive decay and what is disintegration per minute per gram?

 

[Homer Simpson]

as far as the last part, what is disintegration per minute per gram -

its just how many radioactive c-14 atoms are disintegrating into stable N-14 atoms per minute, per gram. If you have twice as many grams, there will be twice as many radioactive decays going on.

The radioactive c14 is created by a reaction with the sun's rays and normal nitrogen in the atmosphere. A plant absorbs this radioactive carbon through photosynthesis while it is alive. When it dies this C14 begins to decay. After 5730 years, half of it will be decayed. After another 5730 years another half will be decayed (1/4 of the orginal amount). Then 1/8 , 1/16 etc.

So its an exponential curve when you plot out how many disintegrations are occurring at different dates. That's what those formulas represent. So plug the nums in and you should come up with something.

 

[Homer Simpson]

Here is a graph of the decay. At the very left side the tree has just died. They know about how much C14 is in it at that time. My measuring how much C14 is in it years after, you can approx its age. You measure this by counting how many disintigrations per minuit per gram are occurring.


http://www.physlink.com/Education/AskExperts/Images/ae403a.gif

ddd

use this site for the math

http://math.usask.ca/emr/examples/expdeceg.html

 

[dumbadum]

thank you!