When rebirthing becomes available, making about 50 Coins results in earning 0.10 Rebirth Points.

Much later in the game, I am seeing about 1.2 million Coins to get 1.0 Rebirth Points.

I have paid to get 1.0 RP per level, so I understand that bit.

But, what determines how many Coins are needed to complete one Rebirth level?

I have started a completely new game, and the number of Coins needed to gain Rebirth Points seems to be creeping up.  It seemed to be 50 at the start, but gone up to about 55 in the time it took me to write this.

At the start of the game, it looks as though it starts at 40 Coins then goes up at about 0.5 Coins at each level,