Looking for a name of a formula...if there is one for this.

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While recieving rehabilitation for a back injury, my therapist was trying to explain the path my recovery is taking.
He said that there was possibly a mathematical formula for it....but nevertheless:

When I began my rehab., I was making extremely fast gains toward recovery. As I progress closer to being 100%, the time by which I approach that end slows.

Similar effects are seen with weight loss, and muscle mass gains. You see the biggest results in the initial phases, but progress slows as the goal comes nearer.

Is there a name for this process?

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Learning curve?

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I know the point you are reaching is called a plateau, but I'm not sure if a formula for the process of recovery exists.

Initially, I would assume that all types of phsyiological gains follow along some sort of natural logarithmic line. I don't know of any studies done on the matter, but do a google on it, there is probably a medical journal or two which have done studies on the predictability of rehabilitation.

Good Luck.

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Law of Diminishing Returns, and I don't think it can be quantified

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Exponetial Decay
You might try the exponential decay formula.

f(t) = C ( 1 - e^(-t/k) )

where C is the final value and k is the time constant. Typically, you assume you have reached the target value after five time constants.

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roger wrote:

Law of Diminishing Returns, and I don't think it can be quantified

I learned it in economics as diminishing marginal returns, more theory I gathered than law, and I never heard of a way to measure it either, although engineer's post is intriguing.

Like pornography, you know it when you experience it, as you have with your rehab, candid.

The example we were presented was with a sack of hamburgers. The second Big Mac consumed is marginally less satisfying than the first, the third less than the second, and so on.

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Thanks all...
Much appreciated.

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Scroll down to "a family of equations"

http://www.swcp.com/raccoon/learncurve.html

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Quote:

I learned it in economics as diminishing marginal returns, more theory I gathered than law, and I never heard of a way to measure it either, although engineer's post is intriguing.

Law of dimishing marginal utility, but I don't think it's the same as the rehab stuff, because in this law, the marginal utility can become a negative number, and I don't think you'd get worst during rehab. I wouldn't know though Laughing

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Sigmoid Curve

Rap

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Ray wrote:

Law of dimishing marginal utility, but I don't think it's the same as the rehab stuff, because in this law, the marginal utility can become a negative number, and I don't think you'd get worst during rehab. I wouldn't know though .

For some reason I was always reminded of that "I Love Lucy" episode where she's working on the chocolate assembly line, which gets faster and faster until Lucy's finally stuffing chocolates into her mouth.

Perhaps that's an example of negative marginal utility. :wink:

(That, or throwing up the hamburgers you've eaten.)

And the math majors obviously have quantified it (thanks rap, stuh, and engineer).

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Actually I made a mistake. You're right, it is the Law of Diminishing Returns which is not the same as the Law of Diminishing Marginal Utility.
I don't think there's a negative number for the former.

Edit: there is a negative number for the former. Laughing

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Looking for a name of a formula...if there is one for this.

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