Question

Explain Logistic Growth with equation.

Hint:

Exponential = J-shaped (unlimited resources). Logistic = S-shaped (limited resources, carrying capacity).

Answer 1

Step 1: Definition.
Logistic growth describes population growth when resources are limited. Initially, population grows rapidly (exponential), but later slows down and stabilizes at a maximum value called the carrying capacity (K).

Step 2: Logistic growth curve.
\[\begin{array}{rl} \bullet & \text{Shape: S-shaped (sigmoid curve).} \\ \bullet & \text{Phases:} \\ \bullet & \text{Lag phase – slow growth.} \\ \bullet & \text{Exponential phase – rapid growth.} \\ \bullet & \text{Deceleration phase – growth slows due to competition.} \\ \bullet & \text{Stationary phase – population stabilizes at carrying capacity.} \\ \end{array}\]

Step 3: Logistic growth equation.
\[ \frac{dN}{dt} = rN \left( \frac{K - N}{K} \right) \] Where: \[\begin{array}{rl} \bullet & \text{\( \frac{dN}{dt} \) = rate of population growth.} \\ \bullet & \text{\( r \) = intrinsic rate of natural increase.} \\ \bullet & \text{\( N \) = population size at time \( t \).} \\ \bullet & \text{\( K \) = carrying capacity of the environment.} \\ \end{array}\]

Step 4: Conclusion.
Logistic growth is more realistic than exponential growth as it considers limited resources and carrying capacity.