I would like to understand calculations made by qPCR software. I create a standard curve in Excel with same parameters as in software with equation for my target: y=-1.571ln(x)+39.433 and calculate CN from exactly same Ct (same decimal places).

x (CN)=((y(Ct)-39,433)/1.571)^e; where (e=2.71828183), and after normalization against used amount (ng) and genome size, I get average CN=8.69, but software result is 8.71. 

Then I try equation used in the software :  Ct=m[log(Qty)]+b, from that x=10^((Ct-b)/m), where b is y-intercept (= 39.433 in this case); m=slope. I get similar results, but not exactly the same average: CN=8.72.

where I'm wrong? are there additional corrections or coefficients usually used in the qPCR calculations by software for absolute quantification?

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