Logistic Model Curve

Logistic Model Curve

Equation:

$$y(t)=\frac{K}{1+e^{-r(t-t_0)}}$$

• K: Carrying capacity (maximum possible value)
• r: Growth rate
• $t_0$: Inflection point (time at which growth is fastest)

Characteristics:

• Symmetric S-curve around the inflection point
• Growth slows as it approaches K due to saturation
• Easy to interpret: K directly gives maximum potential size

Use Cases:

• When saturation is symmetric around the midpoint
• Customer adoption where growth initially accelerates, then decelerates evenly

Related:

• Customer Growth Modeling