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August 13th, 2007, 12:10 PM   #1
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S-curve equation

Can anyone provide info on how I can describe an S-curve with equations? I'm trying to describe a curve that drops below the x-axis and then rises up above and then levels off.

Do I use Richards' or Loretnz' curve or something else?
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August 13th, 2007, 01:09 PM   #2
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How about f(x)=x/cosh(x), where cosh(x):=(e^x+e^-x)/2 is the hyperbolic cosine function? Is that the type of curve you were thinking about? What size do you want the s-curve to be? Specifically, if the highest part of the graph is at (x_0,y_0), then what (approximate) values do you want for x_0 and y_0?
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August 13th, 2007, 02:32 PM   #3
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Hmmm never thought about it that way - its a start but the curve is not likely to be as rigid as this. Basically the x-axis represents time and the y-axis represents cash - it is essentially a cashflow profile over time.
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August 13th, 2007, 02:46 PM   #4
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Could yoube a little more specific in terms of what you want in your s-curve? I assume that you are looking for an approximation, rather than an exact curve, and the curve I gave can be adjusted considerably, in terms of position, maximum height, how quickly it drops, etc.
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August 14th, 2007, 06:04 AM   #5
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What is the slope of the curve at the places where it intersects the x-axis?
In terms of those intersections, what are the value of x for the curve's turning points?
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