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 November 5th, 2011, 01:26 PM #1 Senior Member   Joined: Nov 2011 Posts: 101 Thanks: 0 half life of radium question help The half life of radium is 1690 years. If 200g is present now, how long (to the nearest year) till only 85g are present? According to my worksheet example, I'm supposed to do 100=200e^r(1690) 1/2 = e^r(1690) ln 1/2 = r(1690) r = (ln 1/2) / 1690 but my calculator come up with weird # that doesn't look like an answer. For second part, I'm supposed to do 85=200e^rx to get x for years but this r I've got above don't make any sense. help..
November 5th, 2011, 02:36 PM   #2
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Re: half life of radium question help

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 Originally Posted by shin777 The half life of radium is 1690 years. If 200g is present now, how long (to the nearest year) till only 85g are present? according to my worksheet example, I suppose to 100=200e^r(1690) 1/2 = e^r(1690) ln 1/2 = r(1690) r = (ln 1/2) / 1690 but my calculator come up with weird # that doesn't look like an answer for second part i suppose to 85=200e^rx to get x for years but this r i've got above don't make any sense. help..
I don't what your problem is. However, using the expressions you presented I get 2086 years, which looks perfectly reasonable.

 November 5th, 2011, 02:52 PM #3 Senior Member   Joined: Nov 2011 Posts: 101 Thanks: 0 Re: half life of radium question help Can you explain how you did it for me?
 November 5th, 2011, 03:00 PM #4 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond Re: half life of radium question help Your calculation for r is correct. Now solve 85 = 200 * e^(ln(1/2) * t/1690) for t. You should get 2086 as your answer.
 November 5th, 2011, 03:25 PM #5 Senior Member   Joined: Nov 2011 Posts: 101 Thanks: 0 Re: half life of radium question help Oh, I get 2086 too on my calculator when I just put whole thing in. That's weird coz # I get from r by itself didn't make any sense to me. How about 55 = 28(36/2^(t/5)? How do you solve this for t?
 November 5th, 2011, 05:46 PM #6 Newbie   Joined: Nov 2011 Posts: 27 Thanks: 0 Re: half life of radium question help I have this in my head but do not know whether I am right or not 200/(2^(t/1690)) = 85 2^(t/1690) = 200/85 t = 1690*log( 200/85 ; base of log :: 2) = 2086.24627864657
 November 5th, 2011, 07:56 PM #7 Senior Member   Joined: Apr 2010 Posts: 128 Thanks: 0 Re: half life of radium question help How come I get different answer? 1690 years is 1 half life , therefore from 200g to 100g used 1690 years from 100g to 50g needs another 1690 years , so 50g : 1690 , 1g : 1690/50 1g : 33.8 years from 200g to 85g = 1690 + ( 33.8 x 15 ) $=1690 + 507$ $=2197 years$
 November 5th, 2011, 08:02 PM #8 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: half life of radium question help You are assuming a linear decay, when it is actually an exponential decay. That is why your answer differs from the correct one.

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# Half-Life of a radium mathematical calculation

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