Carrying capacity in equation `(dN)/(dt)=rN[K-N/k]` is :

Options

A. r
B. N
C. K
D. rN

Answer

To solve the question regarding the carrying capacity in the equation \((dN)/(dt) = rN[K - N/K]\), we will break down the components of the equation and identify what each symbol represents, particularly focusing on the carrying capacity.

### Step-by-Step Solution:

1. **Understand the Equation**: The equation \((dN)/(dt) = rN[K - N/K]\) represents the logistic growth model. This model is used to describe how populations grow in an environment with limited resources.

2. **Identify the Variables**:
- \(N\): This represents the current population size or density.
- \(r\): This is the intrinsic rate of growth of the population.
- \(K\): This denotes the carrying capacity of the environment, which is the maximum population size that the environment can sustain indefinitely.

3. **Define Carrying Capacity**: The carrying capacity \(K\) is a crucial concept in ecology. It refers to the maximum number of individuals of a particular species that an environment can support without degrading the habitat. In the context of the logistic growth model, as the population \(N\) approaches \(K\), the growth rate decreases, reflecting the limitations imposed by resources.

4. **Conclusion**: In the equation, the carrying capacity is represented by the symbol \(K\). Therefore, the carrying capacity in the given equation is \(K\).

### Final Answer:
The carrying capacity in the equation \((dN)/(dt) = rN[K - N/K]\) is represented by \(K\).

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