Which one is accurate?

In an unofficial Japanese wiki, I tried to show how to estimate hit points after n days by applying the sum of a geometric progression formulas.

However, as shown in the attached image, the official wiki and the explanation in the game showed different numbers as common ratios.

So I am confused.

Because official wiki said 15%, a calculation of 15% is adopted now at the said informal wiki tentatively, if it's not too much trouble, It would be happy if developer may tell me the correct value.

I think it is an approximated value.

Really?

Supposing you said, I would rather know the error range or coefficient.