My Math Forum What did I do wrong in my solution?

 Differential Equations Ordinary and Partial Differential Equations Math Forum

 May 1st, 2017, 06:46 PM #1 Senior Member   Joined: Apr 2008 Posts: 172 Thanks: 3 What did I do wrong in my solution? A certain radioactive substance has a half-life 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: CA Posts: 1,199 Thanks: 611 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.

 Tags solution, wrong

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post babaliaris Calculus 3 August 28th, 2016 03:08 AM szz Differential Equations 3 December 28th, 2014 08:18 PM dennisdixon Algebra 1 January 18th, 2013 12:09 AM Regnes Algebra 2 January 19th, 2012 10:58 PM TreeTruffle Algebra 2 March 27th, 2010 01:22 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top