
Differential Equations Ordinary and Partial Differential Equations Math Forum 
 LinkBack  Thread Tools  Display Modes 
May 1st, 2017, 06:46 PM  #1 
Senior Member Joined: Apr 2008 Posts: 175 Thanks: 3  What did I do wrong in my solution?
A certain radioactive substance has a halflife period of 35 days. How long will it take a 2 gram sample to decay to 0.05 grams? my solution dy/dt = ky where y is the amount of the substance Solving it gives lny=kt+c  (1) When t=0 days, y= 2 grams. So, plugging them into (1) above gives c=ln2 lny = kt + ln2 When t=35 grams, y=1 day. Next, I use the values to find k and get k=ln2/35 So, lny=  (ln2)t/35 +ln2  (2) When y = 0.05 grams, I plug it into (2). t=186 days. This is wrong. The correct answer is 167 days. I cannot get the answer. Can someone help me? Thanks. 
May 1st, 2017, 07:43 PM  #2 
Senior Member Joined: Sep 2015 From: Southern California, USA Posts: 1,403 Thanks: 713 
I find $k=\dfrac{\ln(2)}{35}$ just as you do and I get 186.267 days for 2g to decay to 0.05g. I think your answer key is mistaken. 
June 28th, 2017, 09:01 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,647 Thanks: 680 
Given that this substance "has a half life of 35 days", we can write $\displaystyle y(t)= A(1/2)^{t/35}$ where A is the original amount and t is in days. The original amount was 2 grams so $\displaystyle y(t)= 2(1/2)^{t/35}a$. To determine when it is reduced to 0.05 grams, solve $\displaystyle 2(1/2)^{t/35}= 0.05$. Divide both sides by 2: $\displaystyle (1/2)^{t/35}= 0.025$. Take the logarithm, base 10, $\displaystyle (t/35)log(1/2)= (t/35)log(2)= log(0.025)=1.602$. Since log(2)= 0.3010, t/35= 1.602/.3010= 5.322 and t= 35(5.322)= 186.2 days. 

Tags 
solution, wrong 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
What is wrong with my solution? (Series Exercise)  babaliaris  Calculus  3  August 28th, 2016 03:08 AM 
What's wrong with my solution ?  szz  Differential Equations  3  December 28th, 2014 07:18 PM 
what's wrong with my solution?  dennisdixon  Algebra  1  January 17th, 2013 11:09 PM 
What am I doing wrong in this basic equation? Or am I wrong?  Regnes  Algebra  2  January 19th, 2012 09:58 PM 
trying to make a solution (liquid solution...) problem...  TreeTruffle  Algebra  2  March 27th, 2010 01:22 AM 