My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
August 7th, 2008, 02:45 PM   #1
Newbie
 
Joined: Aug 2008

Posts: 1
Thanks: 0

Half-life problem. Please help :)

Guys,

Could you please help me with this problem?

"What is the half-life of a radioactive substance that has a decay rate of 25% per decade?

Hint: Remember that the Rule of 70 does not give a good approximation to half-life when the rate is larger than 15%. We must use the actual formula here."

Thanks a bunch..
c47v3770 is offline  
 
August 7th, 2008, 03:06 PM   #2
Senior Member
 
Joined: May 2008
From: York, UK

Posts: 1,300
Thanks: 0

Re: Half-life problem. Please help :)

Hi

The total amount of radioactive material remaining in a decay is always given by where K is the starting amount and is some positive constant related to the rate of decay.

If we measure t in years, then since after 10 years there will be 75% of the starting amount, we have the relationship



so



To work out the halflife, we need to find the value of t - call this - that corresponds to the time where the amount remaining is half the initial amount. This can be represented by the formula

so



or

mattpi is offline  
August 8th, 2008, 09:53 AM   #3
Global Moderator
 
Joined: Dec 2006

Posts: 20,747
Thanks: 2133

If the half-life is t years, (3/4)^(t/10) = 1/2, so t = 10ln(1/2)/ln(3/4) = 24.1 to 3 significant figures.
skipjack is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
halflife, problem



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Half Life allylee Algebra 1 March 8th, 2013 05:26 AM
Half-Life Lucida Algebra 1 March 27th, 2012 02:35 PM
Half life of N2? usyer Physics 3 June 4th, 2011 05:47 PM
Half life Mustangguy93 Calculus 1 October 11th, 2009 02:56 PM
Half-Life symmetry Algebra 3 July 7th, 2007 09:59 AM





Copyright © 2019 My Math Forum. All rights reserved.