idea on closeness defined
TKHunny: thanks for the ideas. My definition of closeness would be to define a region of greatest interest within the entire x=15 to 300 range,
say x= from 15 to 75, and find the % error at each integer value of x compared to the result from the first equation.
Whether the point generated by the second equation was above or below the point generated by the first equation wouldn't matter, only the % error.
A curve from the 2nd equation that never touched the curve from the first equation but always stayed within say 7% would be better than a curve that had approx same values in one segment of the curve but was off by 15% at other segments.
I've been using Microsoft Excel and varying T and d. I've seen that varying d does little to the shape of the curve, but does change it's offset above the x axis.
Changing T through a large range changes both the value it approaches
asymptotically, and the shape/slope a lot. If anyone is interested you can email me at firstname.lastname@example.org, and I can send you the MS Excel files for some varying T values.