Harrier Cooldown

Curious since it there's a margin of error that might mean my formulae are wrong.

Which formula is the correct one:

H(c)=8*(0.99)^(c)

or

H(c)=8*e^(-0.01c)

or another one?

As an aside if a Rioter could answer, what was the thought process of making Harrier's cooldown continuous (or discretely or another type) compounded as opposed to simply be linear haste-base (making 100% halving the cooldown) like how attack speed works with attacks per second and seconds per attack?