What's the multiplier amount that sets each price of an upgrade?

The exact number for multiplying is 1.06. Here's how I got it:

There's a wiki for this game for whatever reason and I decided to collect price data for the upgrades, which comes from the third column of the tables.

I decided to take the numbers for Produce Department, Bakery & Butcher Shop, and here are the results from LVL 2-10.

Produce Department

2-3 = 1.06
3-4 = 1.0599056603773584905660377358491
4-5 = 1.0600801068090787716955941255007
5-6 = 1.0600335852225020990764063811923
6-7 = 1.059801980198019801980198019802
7-8 = 1.0601644245142002989536621823617
8-9 = 1.0599224532957349312654212195982
9-10 = 1.0601928832723644828732956434985

Bakery

2-3 = 1.06
3-4 = 1.0660377358490566037735849056604
4-5 = 1.0619469026548672566371681415929
5-6 = 1.0666666666666666666666666666667
6-7 = 1.0625
7-8 = 1.0661764705882352941176470588235
8-9 = 1.0620689655172413793103448275862
9-10 = 1.0649350649350649350649350649351

Butcher Shop

2-3 = 1.068
3-4 = 1.0655430711610486891385767790262
4-5 = 1.0667838312829525483304042179262
5-6 = 1.067545304777594728171334431631
6-7 = 1.0663580246913580246913580246914
7-8 = 1.0680173661360347322720694645441
8-9 = 1.0663956639566395663956639566396
9-10 = 1.0673443456162642947903430749682

So they're all pretty close to 1.06, so it seems reasonable that the exact number should be 1.06. Though this is not the most accurate, so there could be a formula somewhere, but I don't know how to access the in-game code.

Whatever the case, the result will always be somewhere around 1.06.