Verhulst-pearl logistic growth patten is

Options

A. sigmoid
B. j-shaped
C. straight line
D. hyperbola

Answer

### Step-by-Step Solution:

1. **Understanding Growth Patterns**:
- There are two primary types of growth patterns in populations: exponential growth and logistic growth.
- Exponential growth occurs when resources are unlimited, leading to a rapid increase in population size.

2. **Defining Logistic Growth**:
- The Verhulst-Pearl logistic growth pattern accounts for limited resources in an environment.
- It illustrates how population growth slows as it approaches the carrying capacity of the environment.

3. **Phases of Logistic Growth**:
- **Lag Phase**: Initially, the population grows slowly as it establishes itself in the environment.
- **Log Phase**: Following the lag phase, there is a period of rapid growth as resources are utilized effectively.
- **Stationary Phase**: Eventually, the population growth levels off as resources become limited, and the population reaches its carrying capacity (K).

4. **Mathematical Representation**:
- The logistic growth can be represented by the equation:
\[ \frac{dn}{dt} = rN \left(1 - \frac{N}{K}\right) \]
- Here, \( \frac{dn}{dt} \) represents the rate of change of the population size, \( r \) is the intrinsic growth rate, \( N \) is the current population size, and \( K \) is the carrying capacity.

5. **Shape of the Growth Curve**:
- The logistic growth pattern is visually represented by a sigmoid curve, which has an S-shape.
- This curve shows the slow initial growth, followed by rapid growth, and then a plateau as the population stabilizes at the carrying capacity.

6. **Conclusion**:
- The Verhulst-Pearl logistic growth pattern is characterized by a sigmoid curve, indicating the limitations imposed by resource availability on population growth.