`(dN)/(dt) rN` equation is applicable to …………..population growth.

Options

A. Exponential
B. Logistic
C. Both (a) and (b)
D. Not related to population

Answer

To solve the question regarding the equation \((dN)/(dt) = rN\) and its applicability to population growth, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Equation**: The equation \((dN)/(dt) = rN\) represents the rate of change of a population (N) over time (t). Here, \(dN/dt\) indicates how the population size changes with time.

2. **Identify the Variables**:
- \(N\): Represents the population size.
- \(r\): Represents the intrinsic growth rate or biotic potential of the population, which indicates how quickly the population can grow under ideal conditions.

3. **Analyze the Growth Type**: This equation describes exponential growth, which occurs when resources are unlimited, and the population can grow without any constraints.

4. **Graphical Representation**: The graph of this equation would show an exponential curve, indicating that as time progresses, the population increases rapidly. This is characterized by a J-shaped curve.

5. **Conclusion**: Based on the analysis, the equation \((dN)/(dt) = rN\) is applicable to **exponential population growth**.

### Final Answer:
The equation \((dN)/(dt) = rN\) is applicable to **exponential population growth**.

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