What is the exponential (or geometric) rule (or law) for uranium enrichment? Uranium ore starts at about .72% U-235...
At ~20% U-235, it is considered to be about '90% of the way' to weapons-grade uranium, which is about ~90% U-235...
Because uranium enrichment in centrifuges follows a geometric (or exponential) law...
I have read about this repeatedly when hearing about Iran's enrichment program....
Does anybody know what the 'rule' or 'equation' is for uranium enrichment...
(I am not trying to build a bomb, I swear....)
Edit: P.S.:
In the Work equation $W_extract = -T R ln(x)$ , what are T, R, and x?
I can find that equation nowhere else....
 A: You are basically trying to sort the atoms, reducing entropy. The minimum work per mole of extracting an element that has mole fraction $x$ is
$$W_{extract}=-TR\ln(x).$$
So, the cost difference as you go from $x$ to $2x$ is (assuming $x<1/2$) $$W_{extract}(2x)-W_{extract}(x)=-TR\ln(2).$$ Which is constant, as the exponential law says.
Now, for a mixture of two isotopes we need to account for the work of separating each. $$W_{allextract} = -TR \sum_i x_i \ln(x_i)$$ So for two isotopes the  total energy cost is $$W=-TR [x\ln(x)+(1-x)\ln(1-x)]$$ which has a maximum for $x=1/2$ (maximal entropy). At this point the reader may well get suspicious: why is it getting easier as $x\rightarrow 1$? The answer is that the above formula assumes a process that keeps entropy constant and is close to reversible. This is a bad approximation as we approach the limit, unless we also want the process to take a very, very long time. For imperfect separation and irreversible processes the cost is higher.
A: The exponential law for enrichment is that doubling the percentage of U-235 requires the same amount of effort regardless how much there already is. Getting from 20% to 40% is just as hard as getting from 1% to 2%.
Though obviously, this only works well when the percentage is below half. Getting from 95% to 99% is a lot of work. In this regime, the law goes the other way, i.e. halving the remaining amount of U-238 requires the same amount of work, regardless how much remains.
A: The equation you are looking for is the SWU calculation (Separative Work Units).  The calculations are described at:
https://energyeducation.ca/encyclopedia/Separative_work_unit
Figure 1 shows the exponential dependence that you describe.  Enriching from natural to 4-5% takes more energy then going from 4-5% to 95%.
