Which of the following equations depicts Verhulst-Pearl logistic population growth?

Question

Accepted Answer

B. 1. **Recall the logistic growth model**: This model describes population growth that slows down as the population approaches the carrying capacity $K$, unlike exponential growth which has no such limit.

2. **State the correct equation**: The Verhulst-Pearl logistic growth equation is defined as:
$$
\frac{dN}{dt} = rN\left(\frac{K-N}{K}\right)
$$

Here, $N$ is the population size at time $t$, $r$ is the intrinsic rate of natural increase, and $K$ is the carrying capacity.

3. **Why this form makes sense**: When $N$ is small compared to $K$, the term $\frac{K-N}{K}$ is close to 1, so growth is nearly exponential.

As $N$ approaches $K$, the term $\frac{K-N}{K}$ approaches 0, so growth slows down and eventually stops.

4. **Eliminate incorrect options**: Options A, C, and D use incorrect combinations (such as $K+N$ instead of $K-N$, or dividing by $N$ instead of $K$), which do not represent this braking effect correctly.

Hence, the answer is **Option B**.