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 [itex]y= Cx^{-1}[/itex]

berkeman

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.