Equation of the line for a second order decay

[Miffymycat]

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!

 

[HallsofIvy]

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 y= Cx^{-1}

 

[berkeman]

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!

What about y = A/x ?


EDIT -- Oops, beaten out by Halls again!

 

[Miffymycat]

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?

 

[nasu]

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.

 

[Miffymycat]

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!

 

[Miffymycat]

doh ... again I mean y halves as the x INTERVAL doubles! Sorry