Help With Progression System

Hello everyone. I am trying to find a progression formula that can create a similar effect to the one in the game “Beeface”. Check out this image:

It starts with increments of 5, then 10, then 20 and then it looks like a 1.2x, 1.3x, 1.5x, 2x

How does it go from linear to exponential I guess? Or is it just exponential? I am not great with understanding how math works here so an in depth explanation if you understand the topic would be very helpful

Any guidance is appreaciated!
Thanks,
Mutrix

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