1) Price starts at 50

2) Every time you buy a tile, the price goes up 5

3) This increase is global
4) The culture expansion is tiered (I don't know how its calculated)
5) Each expansion tier multiplies the price (1x, 2x, 3x, 4x)
5.1) Buy tile in closest city (it will be in a lower tier)
6) Cultural expansion is unaffected by buying
7) Try to buy all current tier tiles in a city when buying
8) Buy less tiles situationally
starting cost:
Tier 1 50

Tier 2 100

Tier 3 150

Tier 4 200

Tier 5 I've never seen Tier 5s
...after buying one tile
Tier 1 55

Tier 2 110

Tier 3 165

Tier 4 220

... first screenshot
Tier 1 85

Tier 2 170

Tier 3 255

Tier 4 340

note: Tier 4 is next to a Tier 2 (I don't know why)
Cultural expansion in 6 turns
... second screenshot (after buying both tier 1 tiles)
Tier 1 95

Tier 2 190

Tier 3 285

Tier 4 380

(none available to buy)
Cultural expansion unchanged (6 turns)