My Math Forum  

Go Back   My Math Forum > College Math Forum > Differential Equations

Differential Equations Ordinary and Partial Differential Equations Math Forum

Thanks Tree2Thanks
  • 1 Post By romsek
  • 1 Post By Country Boy
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 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


lny = kt + ln2

When t=35 grams, y=1 day. Next, I use the values to find k and get


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.
davedave is offline  
May 1st, 2017, 07:43 PM   #2
Senior Member
romsek's Avatar
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.
Thanks from topsquark
romsek is online now  
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.
Thanks from topsquark
Country Boy is offline  

  My Math Forum > College Math Forum > Differential Equations

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

Copyright © 2017 My Math Forum. All rights reserved.