I am doing graduate research on chemical production rates, and I need to reproduce a logistic decay function. I have an upper and lower limit, 3 points and an inflection point:
Upper limit: $3.3$
Lower limit: $1.2$
3 points: $(7.5, 3.3)$, $(15.258, 1.3)$, $(16, 1.2)$.
Inflection point: $(11.6, 2.25)$.
It seems too easy, but hours of searching the internet (including this site) have yielded no results on how to make this equation. Sorry if this is a duplicate question.
$$ \begin{array}{cc} \hline \text{Approximation} & \text{Function} \\ \hline \text{polynomial} & 0.014473825 x^2 - 0.58719371 x + 6.8898002\\ \text{exponential} & 8.0799808\cdot 0.88741028^x\\ \text{linear} &-0.25145441x + 5.1819567\\ \text{logarithmic} & -2.7909806\ln(x) + 8.922503\\ \hline \end{array} $$