Finite-baryon-fraction correction to a constant-offset catch-up mode

With growing total matter mode, constant relative offset, initial ${\Delta }_B=0$, and $x=R/R_r$, the exact ratio is ${\Delta }_B/{\Delta }_D=f_D(x-1)/(f_{D}x+f_B)$. It reduces to $1-x^{-1}$ only in the dark-matter-dominated limit.