This piece really helped me. E * R =constant. I tested this on EOS, Telos and BOS and is exactly right. This formula also has no slippage.

price = dE/-dR = d (c/R)/-dR= -c/(R*R) dR/-dR = E/R -> QED

PS it is -dR instead of dR as RAM connector buffer goes down when EOS enters the EOS connector

You can also easily derive what the price curve looks like if you want to plot on the X-axis the % RAM utilisation = x and on the Y-axis the price = p

p = E / R and R = (1-x) * R0 and E0 * R0 = c (E0 and R0 are starter balances)
p= c / (R^2) = E0 * R0 / ((1-x)^2 * R0^2) = E0/R0 /(1-x)^2 =p0 / (1-x)^2

So the price p goes up from the starting price p0 with the curve 1/(1-x)^2 in every Bancor Relay model