Class 12 NEET Biology Organisms and Populations

Concept:Logistic population growth describes how a population initially grows exponentially but slows as it approaches the carrying capacity of the environment.Key Fact:The Verhulst-Pearl logistic equation includes a term $\frac{K-N}{K}$ that reduces the growth rate as population size $N$ approaches the carrying capacity $K$.Explanation:The logistic growth equation is $\frac{dN}{dt} = rN \left( \frac{K-N}{K} \right)$.Here, $r$ is the intrinsic rate of natural increase.$N$ is the current population density at time $t$.$K$ is the carrying capacity of the environment.The factor $\frac{K-N}{K}$ represents the fraction of carrying capacity still available.When $N$ is small, $\frac{K-N}{K}$ is nearly $1$, so growth is almost exponential.When $N$ approaches $K$, the factor becomes close to zero, slowing growth.The correct equation must have $(K-N)$ in the numerator and $K$ in the denominator.Only option B matches this form exactly.Options A, C, and D have incorrect algebraic structures that do not represent logistic growth.Answer:Option B: $\frac{dN}{dt}=rN\left(\frac{K-N}{K}\right)$.