LOGISTIC GROWTH X Logistic curves, not exponential fantasies, better reflect how real systems grow and mature

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Logistic growth is a type of growth that starts fast but eventually slows down and levels off as it reaches a limit, often called the carrying capacity.

🔍 Definition:

Logistic growth occurs when the rate of population or system expansion decreases as it approaches a maximum sustainable size, due to limited resources, space, or other constraints.

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📈 Logistic Growth Curve:

• The shape of the curve is S-shaped (sigmoid).

• Phases:

  1. Lag phase: Slow initial growth.

  2. Exponential phase: Rapid, accelerating growth.

  3. Deceleration phase: Growth rate slows.

  4. Stationary phase: Growth levels off at the carrying capacity.

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🧪 Formula:

$$P(t) = \frac{K}{1 + \frac{K - P_0}{P_0} e^{-rt}}$$

Where:

• $P(t)$ = population (or value) at time $t$

• $K$ = carrying capacity

• $P_0$ = initial population

• $r$ = growth rate

• $e$ = Euler’s number (≈ 2.718)

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🌍 Real-World Examples:

• Biology: Bacteria in a petri dish—grow fast, then slow as resources run out.

• Technology: Adoption of smartphones or electricity—starts slow, peaks, then saturates.

• Economics: Urban population growth in a city eventually hits limits like land or infrastructure.

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✅ Key Insight from Smil:

"Logistic curves, not exponential fantasies, better reflect how real systems grow and mature."

Let me know if you’d like a visual of the curve or examples in a specific domain (tech, biology, economy).

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