NEET 2025 — Biology solution

NEET2025Biology

Which one of the following equations represents the Verhulst-Pearl Logistic Growth of population?

A
$\frac{d N}{d t} = N (\frac{r - K}{K})$
B
$\frac{d N}{d t} = r (\frac{K - N}{K})$
C
$\frac{d N}{d t} = r N (\frac{K - N}{K})$
D
$\frac{d N}{d t} = r N (\frac{N - K}{N})$

Solution

Verhulst-Pearl logistic growth describes a population that grows rapidly when small but slows as it approaches the environment's carrying capacity $K$ :

$\frac{d N}{d t} = r N (\frac{K - N}{K})$

Here $r$ is the intrinsic growth rate, $N$ is the population size, and the term $\frac{K - N}{K}$ shrinks toward 0 as $N \to K$ , producing the characteristic sigmoid curve.

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