Hope this one helps. Removed the floor function as that one seems to truly confuse you while its sole purpose was to take away confusion for the average user, so if it confuses you it loses its purpose.

The blue line is the current linear reward n -> c.

The brown, pink and gray line are the linear convergent rewards Sn/(1+Sn) -> c/(1+Sn) for different values of S.

The orange, green and purple lines are my nS^log(n)-> S^log(n+c) lines for different values of S.

Again, note that the scale for X is logaritmic, while the Y axis is linear and conveys the reward per unit of influence in order to clearly demonstrate the scaling properties of the reward scaling functions.