Logistic function passing through two points? Quick formulation of the problem:
Given two points: $(x_l, y_l)$ and $(x_u, y_u)$
with: $x_l < x_u$ and $y_l < y_u$,
and given lower asymptote=0 and higher asymptote=1,
what's the logistic function that passes through the two points?
Explanatory image:

Other details:
I'm given two points in the form of Pareto 90/10 (green in the example above) or 80/20 (blue in the example above), and I know that the upper bound is one and the lower bound is zero.
How do I get the formula of a sigmoid function (such as the logistic function) that has a lower asymptote on the left and higher asymptote on the right and passes via the two points?

To elaborate on the accepted answer, if we have a logistic function using the common notation:
$$f(x) = \frac{1}{1 + e^{-k(x-x_0)}}$$
... and we want to solve for $k$ and $x_0$ given two points, $(x_l, y_l)$ and $(x_u, y_u)$:
First we can group the unknowns in a single term $b \equiv k(x-x_0)$.  So:
$$y = \frac{1}{1 + e^{-b}}$$
$$y(1 + e^{-b}) = 1$$
$$e^{-b} = \frac{1-y}{y}$$
$$-b = \ln\left(\frac{1-y}{y}\right)$$
$$ b = \ln\left(\frac{y}{1-y}\right)$$
Now we expand b:
$$k(x-x_0) = \ln\left(\frac{y}{1-y}\right)$$
... which gives us a linear system to solve for $k$ and $x_0$ given the values of two $(x, y)$ coordinates.
