Carbon DatingDate: 05/27/99 at 07:33:49 From: Vicky Subject: Decay (Carbon Dating) Bones A and B are x and y thousands years old respectively. Bone A contains three times as much Carbon-14 as bone B. What can you say about x and y? Date: 05/27/99 at 10:24:29 From: Doctor Anthony Subject: Re: Decay (Carbon Dating) If r = ratio of carbon-14 to carbon-12 then, if we take r = 1 in living material (say branch of a tree) then with the half-life of 5730 years we have: In 5730 years the value of r is down to 1/2 So we have the equation r = (1/2)^(t/5730) where t = time in years. With this equation we can see that t = 0 gives r = 1 " t = 5730 gives r = 1/2 " t = 11460 gives r = 1/4 and so on. So for bone A we have r(A) = (1/2)^(x/5730) and for bone B we have r(B) = (1/2)^(y/5730) and we are told r(A) = 3*r(B) (1/2)^(x/5730) = 3*(1/2)^(y/3730) (1/2)^(x/5730 - y/5730) = 3 and taking logs (x-y)/5730 ln(1/2) = ln(3) (x-y)/5730 = ln(3)/ln(1/2) (x-y)/5730 = -1.584962 x - y = -9082 x = y - 9082 and so bone A is about 9000 years younger than bone B - Doctor Anthony, The Math Forum http://mathforum.org/dr.math/ |
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