My Math Forum How do I find the half-life

 Calculus Calculus Math Forum

 November 17th, 2017, 04:49 PM #1 Newbie   Joined: Nov 2017 From: United States Posts: 1 Thanks: 0 How do I find the half-life In 2 years, 20% of a radioactive element decays. Find its half-life rounded to 2 decimal places. I think k=LN(0.20)/2, but I'm unable to figure out how to solve for the half-life.
 November 17th, 2017, 04:57 PM #2 Math Team   Joined: Jul 2011 From: Texas Posts: 2,771 Thanks: 1426 $0.8 = \left(\dfrac{1}{2}\right)^{2/h}$ solve for the half-life, $h$
 November 17th, 2017, 05:42 PM #3 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 I prefer to write any problem involving "half life" as powers of 1/2. Since skeeter beat me to that, here is how to do it in a more "formulaic" method. Any such problem (constant rate of decay) can be written in the form $S(t)= Ce^{kt}$. When $t = 0$, $S(0) = C$, the initial amount. When $t = 2$, $S(2) = Ce^{2k}$ and we are told that is $C - 0.2C = 0.8C$, so $e^{2k}= 0.8$. Hence $2k= \ln(0.8)$ or $k= \frac{\ln(0.8)}{2}$. Hence the formula is $\displaystyle S(t)= Ce^{\frac{\ln(0.8)t}{2}}= C\left(e^{\ln(0.8)}\right)^{t/2}= C(0.8^{t/2})$. "Half life" is the value of $t$ that makes that $C/2$. We need to solve $C(0.8^{t/2})= C/2$ or $0.8^{t/2}= \frac{1}{2}$. That is the same as skeeter's solution. Last edited by skipjack; November 17th, 2017 at 07:09 PM.

 Tags find, halflife

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post allylee Algebra 1 March 8th, 2013 05:26 AM usyer Physics 3 June 4th, 2011 05:47 PM jerakahol Algebra 10 January 10th, 2011 03:27 PM Mustangguy93 Calculus 1 October 11th, 2009 02:56 PM symmetry Algebra 3 July 7th, 2007 09:59 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top