The equation for the gradient concentration of Bicoid along the A-P axis is
$$Bcd=[Bcd]0e^{-x_0/\lambda}$$
Where \([Bcd]_0\) is the source concentration, \(x\) is the position along the A-P axis, and \(\lambda\) is the decay length of the exponential function. Changing the number of copies of the Bicoid gene can scale this function, making it into
$$Bcd=D[Bcd]_0e^{-x/\lambda}$$ This can then be manipulated to show that any original feature that is located at \(x_0\) is linearly scaled by \(ln(D)\) to get to its new position.
$$Bcd=D[Bcd]_0e^{-x{new}/\lambda}$$
$$x_{new=Dln(D)+x_0}$$
[[Varying Bicoid in an Embryo]]
Sources
“How the Fly Gets Its Neck.” Accessed: Aug. 28, 2023. [Online]. Available: http://www.rpgroup.caltech.edu/mbl_physiology/code/CephalicFurrow.html