Progressive warp speed for ULTRALONG flights

#1

In large 64p games it may take even a week of warp flight to get ships from one end of your empire to fight an enemy at your other end. There already have been suggestions such as to make warpgates upgradeable, so that collecting ships within this large empires isn’t such a pain, but…
What I propose is to Increase the travel speed of a single Carrier with every consecutive ly traveled between your own warpgates.

I suggest that the time will effectively get (at least) halved from maximum of 7 days, which is what it takes to travel half the galaxy, to 3-4 days.

[size=11]*Now that I look at the picture again, it’s still quite lengthy… A formerly 7d long flight still takes more than 4 days to finish.[/size]

###Preconditions

1. The Carrier MUST travel at warp speed.
2. The Carrier must NEVER stop.
3. You must travel between your own (or allied) warpgated stars.
4. If any of Preconditions is not met, the bonus is lost and counter resetted.

###Propositions

1. The speed increases thrice with every 50 light years traveled.
2. The speed peaks after total of 150 ly has been traveled, which is roughly 6 days ± 6h at hyperspace range 8-10 and 14 jumps of normal warp speed.
3. There is a grace period of 50 ly with the maximum speed before it gets resetted.
4. The total flight length is 200ly.

###EDIT:
At first my suggestion was that the speed increases linearly with every ly traveled after the second day of travel, peaking after fourth day of travel, but it was quite hard to describe mathematically, so I remade it in the process. It now should be more clear.