Results 1 to 2 of 2

Math Help - Linearizing

  1. #1
    Newbie
    Joined
    Sep 2008
    Posts
    8

    Linearizing

    Im in need of some serious help.

    I'm given the problem of the theoretical radioactive decay.

    N=(N0)(e^(-.693t/t))

    It needs to look like y=mx+b
    t= t sub 1/2
    N0= N sub zero
    y=N/No

    This is linearizing equations and I dont even know where to begin. Any help at all?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Aug 2007
    Posts
    144
    Hi Chayned,

    Let's define \lambda = t_{\frac{1}{2}} . We have

    N=N_0\cdot e^{\left(\dfrac{-0.693t}{\lambda}\right)}

    Well a good start would be to log both sides with base e (You will see why in a minute)

     \implies \ln(N)=\ln \left\{N_0\cdot e^{\left(\dfrac{-0.693t}{\lambda}\right)}\right\}

    \implies \ln(N)=\ln(N_0)+\ln \left\{e^{\left(\dfrac{-0.693t}{\lambda}\right)}\right\} Since \ln (ab) \equiv \ln (a) + \ln (b)

    \implies \ln (N)=\frac{-0.693t}{\lambda}+ \ln (N_0) Since \ln (e^a) \equiv a

    \implies \ln (N)=\frac{-0.693}{\lambda} \cdot t + \ln (N_0) Which is of the form y=mx+b where y=\ln (N)~,~m=\frac{-0.693}{\lambda}~,~x=t and b=\ln (N_0)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. linearizing log equations
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: September 13th 2011, 07:12 PM
  2. Polynomial for linearizing a curve
    Posted in the Advanced Applied Math Forum
    Replies: 0
    Last Post: May 12th 2010, 11:02 AM
  3. Linearizing ODE
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: April 2nd 2010, 11:30 PM
  4. linearizing a 2nd order ODE
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: November 16th 2009, 02:02 PM
  5. Linearizing the response
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: March 9th 2009, 05:34 PM

Search Tags


/mathhelpforum @mathhelpforum