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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  
Global Moderator Joined: May 2007 Posts: 6,732 Thanks: 689  Re: half life of radium question help Quote:
 
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: 7,932 Thanks: 1127 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 ) 
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: 520 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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