This is a very general view and quick - as I have a nice Malbec opened and breathing.
In all cases I assume full law knowledge, and basic empathy for what the players are doing.
The step from 9 to 8 is not great for a referee with decent management skills, and general fitness.
The one from 8 to 7 is a big one in management (communication and control) and the game starts getting quicker with fewer errors and much longer cycles of play.
From 7 to 6 nothing in the matches happens by mistake, the management challenge is much higher, spotting trends, escalating and getting early match compliance are crucial. Speed of play and physicality goes up yet again, so the referee must be physically very fit, and mentally attuned at all times with an all round awareness of everything happening on the pitch, and increasing levels of preventative management.
At L5 match speed is up again by a significant amount, major challenges at scrum and breakdown are encountered, consistency is essential, 100% accuracy required, and adaptability to tactical changes in the match. More preventative management, quick judgement and decisions, plus very good fitness levels.
The step up in management, skill and fitness is not simple step each time but increasing at each level, which reflects the standard of players and the games overall.
Enjoy the wine.
But why the use of the words linear and exponential?