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 can follow these steps:

### Step-by-Step Solution:

1. **Identify the Equation**: The given equation is a form of the logistic growth model, which is used to describe how populations grow in an environment with limited resources.

2. **Understand the Components**:
- \(N\): Represents the population size at time \(t\).
- \(r\): Represents the intrinsic growth rate of the population.
- \(K\): Represents the carrying capacity of the environment.

3. **Define Carrying Capacity**: The carrying capacity \(K\) is the maximum population size that the environment can sustain indefinitely. It is the point at which the population growth rate decreases to zero because the resources are fully utilized.

4. **Analyze the Equation**: In the equation, the term \([K - N/K]\) indicates how the growth rate changes as the population \(N\) approaches the carrying capacity \(K\). As \(N\) gets closer to \(K\), the growth rate \((dN/dt)\) approaches zero, indicating that the population has reached its carrying capacity.

5. **Conclusion**: Therefore, in the logistic growth equation \((dN)/(dt)=rN[K-N/K]\), the carrying capacity is represented by the variable \(K\).

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

---