Petz Formulas

Well I'm a math/science major went and found formulas for petz. I've shared these on other forums but decided I'd share on Petzabloo as well with the new table I made for them! I have 2 formulas, the first is for how many petz you need from the adoption center to have a full non-inbred family tree. f(x)=.5(2)^x where x is the generation you want. The second one is the number of ancestors a pet has to have in their family tree to have a full tree g(x)=(.5(2)^x)+((.5(2)^x)-2) where x is generation again and we don't count the pet itself in its family tree. They don't work for 1st gen but I figure that really isn't very important. I also have all the parentheses because if you happen to have a TI graphing calculator you need them.

For those who would like to use the formulas themselves I'm going to do a quick walk through however feel free to skip to the table if you don't want to see the formulas in action.

I'm going to use 3rd gen because that's an easy number to work with.
f(x)=.5(2)^x
Substitute 3 in for x
f(x)=.5(2)³
exponents first so 2X2X2=4X2=8
f(x)=.5(8)
.5X8=4
f(x)=4
So to have a full tree non inbred pet up to gen 3 you need 4 petz from the AC!

g(x)=(.5(2)^x)+((.5(2)^x)-2)
Substitute 3 for x
g(x)=(.5(2)³)+((.5(2)³)-2)
Start with exponents: 2X2X2=4X2=8
g(x)=(.5(8))+((.5(8)-2)
Each parentheses set look at as a separate equation and do multiplication. .5X8=4
g(x)=4+(4-2)
Order of operations: 4-2=2
g(x)=4+2
Now it's simple addition 4+2=6
g(x)=6
A full tree for a 3rd generation pet has 6 ancestors.

Now for the table the first column is the generation, the second is the petz from the AC needed for that generation to have a full non inbred tree, and the third is the ancestors in the full tree. 

I only went to gen 25 however I have no problem going up higher if anyone would like me to. 
If you have a suggestion for something that might be able to have a formula let me know and I'll try to find one or if you have any questions about these formulas just let me know ^^