If Carbon Calculator should shut down, how do we know the percentages vs the years (as portions and multiples of halflife)?

I did a calculation, considering things like 1/8 of a halflife should give a percentage of original quantity corresponding to 8th root of one half. Here is my rough calculation, below is the link I am so often using instead of calculating like this:



And here is the carbon calculator online too:

ppt.li/3m8 being short link for:

Carbon 14 Dating Calculator
https://www.math.upenn.edu/~deturck/m170/c14/carbdate.html