If 'K' is the carrying capacity of the habitat, 'N' is the total number of individuals in a population with intrinsic rate of reproduction as 'r' the growth rate of such a population will be directly proportional to :
I. r.
II. 1/N
III. 1/K-N
IV. (K-N)/K

Options

A. I and II
B. II and III
C. I and IV
D. Only I

Answer

To determine the growth rate of a population in relation to its carrying capacity (K), total number of individuals (N), and intrinsic rate of reproduction (r), we can analyze the options provided in the question.

### Step-by-Step Solution:

1. **Understanding Carrying Capacity (K)**:
- Carrying capacity (K) is the maximum population size that an environment can sustain indefinitely without being degraded.

2. **Understanding Population Size (N)**:
- N represents the current number of individuals in the population.

3. **Understanding Intrinsic Rate of Reproduction (r)**:
- The intrinsic rate of reproduction (r) is the rate at which a population would grow if there were no limits to its growth.

4. **Logistic Growth Model**:
- The growth of a population can be described by the logistic growth model, which is given by the equation:
\[ \frac{dN}{dt} = rN \left(1 - \frac{N}{K}\right) \]
- Here, \(\frac{dN}{dt}\) represents the change in population size over time.

5. **Identifying Proportional Relationships**:
- From the logistic growth equation, we can see that the growth rate \(\frac{dN}{dt}\) is directly proportional to:
- \(r\) (the intrinsic rate of reproduction),
- \(N\) (the current population size),
- \((K - N)\) (the difference between carrying capacity and current population size),
- and inversely proportional to \(K\) (the carrying capacity).

6. **Analyzing the Options**:
- I. \(r\) - **Yes, growth rate is proportional to \(r\)**.
- II. \(1/N\) - **No, growth rate is not directly proportional to \(1/N\)**.
- III. \(1/(K-N)\) - **No, growth rate is not directly proportional to \(1/(K-N)\)**.
- IV. \((K-N)/K\) - **Yes, growth rate is proportional to \((K-N)/K\)**.

7. **Conclusion**:
- The growth rate of the population will be directly proportional to options I and IV: \(r\) and \((K-N)/K\).

### Final Answer:
The growth rate of such a population will be directly proportional to **I. r** and **IV. (K-N)/K**.