The graph in case of a population showing maximum intrinsic growth will be

Options

A. Sigmoid
B. J Shaped
C. S shaped
D. Hyperbola

Answer

To solve the question regarding the graph of a population showing maximum intrinsic growth, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Population Growth Models**:
- There are different models to describe population growth, primarily exponential (J-shaped) and logistic (S-shaped).
- Exponential growth occurs when resources are unlimited, leading to a rapid increase in population size.

2. **Identifying the Graph Types**:
- **Sigmoid (S-shaped)**: This represents logistic growth, which is limited by carrying capacity. It does not show maximum intrinsic growth.
- **J-shaped**: This represents exponential growth, where the population grows rapidly without limits.
- **S-shift and Hyperbolic**: These are not standard terms for population growth graphs and do not specifically indicate maximum intrinsic growth.

3. **Analyzing the J-shaped Graph**:
- The J-shaped graph indicates that the population grows exponentially. The equation for this growth is given by:
\[ \frac{dn}{dt} = rN \]
where \( r \) is the intrinsic rate of natural increase and \( N \) is the population size.
- In this model, as long as resources are unlimited, the population can grow indefinitely, which corresponds to maximum intrinsic growth.

4. **Conclusion**:
- Since the question asks for the graph that represents maximum intrinsic growth, the correct answer is the J-shaped graph, which indicates exponential growth.

### Final Answer:
The graph in case of a population showing maximum intrinsic growth will be **J-shaped**.