Originally Posted by

**capheresy** I'm not sure if this is better suited for an Excel forum, but here goes.

I will know the value of x, which can be anything between 1.00 and 71.32 (inclusive), and can have any number of decimal places to the right, such as 20.123456789.

An x value of EXACTLY 1.00 must return a value of EXACTLY 0.60

An x value of EXACTLY 71.32 must return a value of EXACTLY 1.00

The result values in the continuous range 0.60 to 1.00 must increase at a Decreasing rate. For example,

(1) An x value of around 2 should return a value greater than 0.60, call it z1

(2) An x value of around 70.32 should return a value less than 1.00, call it z2

Because I want a decreasing rate of increase, z1 minus 0.60 should be significantly greater than 1.00 minus z2

It seems like raising x to a power that is in the range 0 to 1 should provide the increase at a Decreasing rate, but nailing down the correct power that enforces both endpoints is where I'm stuck.