The population growth is generally described by the following equation : `(dN)/(dt)= rN ((K-N)/(K))` What does 'r' represent in the given equation ?

Options

A. Population density at time 't'
B. Intrinsic rate of natural increase
C. Carrying capacity
D. The base of natural logarithm

Explanation

To solve the question regarding what 'r' represents in the population growth equation `(dN)/(dt)= rN ((K-N)/(K))`, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Equation**: The equation given is a representation of population growth, specifically the logistic growth model. This model accounts for limited resources, which affects how populations grow over time.

2. **Identify Components of the Equation**:
- **dN/dt**: This term represents the rate of change of the population size (N) over time (t).
- **N**: This is the current population size or density.
- **K**: This represents the carrying capacity of the environment, which is the maximum population size that the environment can sustain due to limited resources.
- **r**: This is the intrinsic rate of natural increase.

3. **Define 'r'**: The intrinsic rate of natural increase (r) is calculated as the difference between the birth rate and the death rate of the population. It indicates how quickly a population can grow under ideal conditions, without any limiting factors.

4. **Conclusion**: Therefore, in the context of the logistic growth model, 'r' is a crucial parameter that reflects the potential growth rate of the population when resources are not limiting.

### Final Answer:
In the equation `(dN)/(dt)= rN ((K-N)/(K))`, 'r' represents the intrinsic rate of natural increase of the population.

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