Read the following text and answer the following question on the basis of the same :
Growth of population with time shows specific and predictable patters. Two types of growth patter of populaiton are exponetial and logistic growth . When resource in the habitat are unlimited each species has the ability to relize fully its innate potential to grow in number . Then the population gorws in exponential fashion . When the resource are limited growth curve shows an inital slow rate and then it accelerates and finally slows giving the gorwth curve which is sigmoid .
The population growth is generally descibed by the following equations :
`dN//dt = rN(K-N)//K`
What does 'r' represent in the given equation ?

Options

A. Population density at time Y.
B. Intrinsic rate of natural increase
C. Carrying capacity
D. The base of natural logarithum

Explanation

To answer the question regarding what 'r' represents in the given equation for population growth, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Equation**: The equation provided is `dN/dt = rN(K-N)/K`. This equation describes the rate of change of a population over time (dN/dt) in relation to its current size (N) and the carrying capacity (K) of the environment.

2. **Identifying the Components**:
- **dN/dt**: This represents the rate of change of the population size over time.
- **N**: This is the current population size.
- **K**: This is the carrying capacity of the environment, which is the maximum population size that the environment can sustain.
- **r**: This is the variable we need to define.

3. **Defining 'r'**: In population ecology, 'r' is known as the intrinsic rate of natural increase. It reflects the potential growth rate of a population under ideal conditions, where resources are abundant, and there are no limiting factors.

4. **Conclusion**: Therefore, in the context of the equation, 'r' represents the intrinsic rate of natural increase, which is essentially the difference between the birth rate and the death rate of the population.

5. **Final Answer**: The correct option is **b. Intrinsic rate of natural increase**.