1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Equation of the line for a second order decay

  1. Jun 26, 2012 #1
    What is it?!! I have tried plotting dummy data showing y values halving as x values double and no simple type of equation results (ie exponential, power, polynomial etc) - is this true? I thought such a standard function would be a simple one!
     
  2. jcsd
  3. Jun 26, 2012 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Yes, it is pretty simple. You are talking about a simple "inverse" proportion: y= C/x or xy= C. When x doubles, that is, x becomes 2x, y must halve in order that the product be constant: (2x)(y/2)= xy= C. If you want to think of that as a "power" it is [itex]y= Cx^{-1}[/itex]
     
  4. Jun 26, 2012 #3

    berkeman

    User Avatar

    Staff: Mentor

    What about y = A/x ?


    EDIT -- Oops, beaten out by Halls again! :biggrin:
     
  5. Jun 26, 2012 #4
    Sorry guys _ I meant that the x value interval doubles eg y = 100, 50, 25, 12.5; x = 0, 10, 30, 70 ie a second order decay where x represents elapsed time ie the half-life of the decay is doubling. Any ideas?
     
  6. Jun 26, 2012 #5
    y=1000/(x+10)
    You can express both x and y as functions of powers of 2 (2^n where n=0,1,2,...).
    Eliminate 2^n to find y as function of x.
     
  7. Jun 22, 2013 #6
    Second order decay - what's the function type?

    Finally found a moment to complete this:

    Second order decay function y = f(x) ie y halves as x doubles

    Eg y = 100, 50, 25, 12.5, 6.25 when x = 0, 10, 30, 70, 150 etc
    so y = 100/2^n and x = (10 x 2^n)/10
    Eliminating 2^n gives y = 1000/(x+10)

    Applying to a second order concentration decay where A is inital concentration, Ao = A at time t=0

    A = Ao [a/(t+a)] where a is a second constant

    What type of function is y = a/(a+x) classed as - hyperbola? inverse? None of these are fitted by Excel

    Thank you to the Mathematicians out there!
     
  8. Jun 22, 2013 #7
    doh ... again I mean y halves as the x INTERVAL doubles!!! Sorry
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Equation of the line for a second order decay
  1. Equation of a Line (Replies: 3)

  2. Second Order Bode Plot (Replies: 1)

Loading...