The equations depicted here describe the transition between states; not the method. In the paragraphs below, the nature of the trades and fees on Bancor, including the Bancor Vortex is described. A portion of the swap revenue is collected and swapped back for BNT atomically, as part of the trade. This is how the contracts behave mathematically. After the vortex fee amount is determined, the swap function is simply called using this number as the input. The equations below are inclusive of all steps, but aren’t featured in the code.