The logistic function is defined by the formula: $$f(x) = \frac{L}{1 + e^{-k(x-x_0)}}$$ where: - \(L\) is the curve's maximum value. - \(e\) is the base of the natural logarithm. - \(k\) is the logistic growth rate. - \(x_0\) is the x-value of the sigmoid's midpoint.
This function is particularly useful for modeling scenarios where growth is limited by environmental factors, making it ideal for catalytic processes.
