If we adjust these streak milestones for how often they occur:

$$\frac{10\sqrt{x} + 500}{12.5}+\frac{30\sqrt{x} + 1500}{100}+\frac{50\sqrt{x} + 2500}{125}+\frac{100\sqrt{x} + 5000}{1000}+\frac{250\sqrt{x} + 12500}{1000}$$ $$= 92.5 + 1.85 \sqrt{x}$$

Then we can use the resulting formula to determine your current battle exp value!
Example: if your current streak is 5000, then each battle you do would grant on average: 200 + 92.5 + √5000 = ~423xp!
This assumes you never tie your battles though, so it's a little optimisitic in that regard.

Charts made by the community featuring more concrete data: