Results 1 to 3 of 3

Math Help - Exponential Decay-Radioactivity

  1. #1
    Junior Member
    Joined
    Sep 2008
    Posts
    27

    Exponential Decay-Radioactivity

    A sample of a radioactive substance decayed to 95.5% of its original amount after a year. What is the half-life of the substance in years, and how long would it take the sample to decay to 25% of its original amount in years.

    My roommate just asked me this and I don't remember how to do it! Please help!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Rhymes with Orange Chris L T521's Avatar
    Joined
    May 2008
    From
    Chicago, IL
    Posts
    2,844
    Thanks
    3
    Quote Originally Posted by acg716 View Post
    A sample of a radioactive substance decayed to 95.5% of its original amount after a year. What is the half-life of the substance in years, and how long would it take the sample to decay to 25% of its original amount in years.

    My roommate just asked me this and I don't remember how to do it! Please help!
    Let N_0 be the original amount of the substance and N be the current amount of the substance.

    Now, radioactive decay takes on the form N=N_0e^{-kt}, where k is the decay constant. We need to know what k is, because the half life of this substance is defined by \lambda=\frac{\ln 2}{k}, where \lambda is the half life.

    -------------------------------------------------------------------------

    The first bit of information gives us enough info to find k.

    It takes a year for the substance to decay to 95.5% of the original amount.

    Thus, we see that N=N_0e^{-kt}\implies .955N_0=N_0e^{-k}, where we replaced N with .955N_0.

    This now simplifies to .955=e^{-kt}\implies \ln(.955)=-k\implies \color{red}\boxed{k\approx 0.046}

    Now we can find the half life:

    \lambda=\frac{\ln 2}{0.046}\implies\color{red}\boxed{\lambda\approx 15.05~\text{years}}

    -------------------------------------------------------------------------

    Now, can you find t, such that .25=e^{-0.046t}?? [this was what the second part of the question was asking for]

    Does this make sense?

    --Chris
    Last edited by Chris L T521; October 14th 2008 at 08:03 PM. Reason: wrong percentage...
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2008
    Posts
    27
    thank you so much!!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. exponential decay
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: July 23rd 2010, 12:03 AM
  2. Decay rates in exponential decay
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: December 21st 2009, 07:20 AM
  3. Exponential Decay
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 17th 2009, 11:45 AM
  4. Exponential decay?
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: May 7th 2009, 11:58 PM
  5. Exponential Decay
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: October 11th 2008, 07:48 AM

Search Tags


/mathhelpforum @mathhelpforum