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

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?