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I'm looking for a way to create a hyperbolic curve. See this sample:

Curve samples

I've entered a start and end value in the yellow cells and the formula should fill in the cells from B2 to B19 automatically. Black is a straight A-B line. It's the green, blue and red curves I'd like to accomplish. The green one is only slightly curved. The blue one increases more at the beginning and less towards the end and the red one does that even more. The blue one I could do with a LOG function like this: =$B$1+((LOG10(A2)/LOG10(20))*($B$20-$B$1)). But I'd also like to be able to create curves that are even more or less curved. Would there be a formula that could do that? A formula that would enable me to edit the curve shape?

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Maybe this works, maybe not. Trial and error shows odd'ish shape when m-value gets pretty low, but maybe this would work better with more X-points. At any rate, this is what I tried. I'm using just 7 points, plus a 0/0 starting point for the chart.

Cell C3 formula: =($G$2*A3)/(A3+$G$1)

Cell D3 formula: =C3/$C$9*7

Drag 'em down.

The k-value in cell G2 doesn't seem to matter here since we're adjusting the values in column D so that you can fit to the same min/max for your chart.

Just adjust the m-value in cell G1 to see the effects of your [Scatter Plot with Line] chart. A higher m-value will have a flatter curve, while a lower m-value will have a steeper curve.

Maybe something can be done with x=1 to make it look a little nicer. But maybe having more points will solve that for you.

enter image description here

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