Sigmoid/logistic growth curve is represented by

Options

A. dN/dt=rN
B. dN/dt=rN(1-N/K)
C. Nt=No+B+I-D-E
D. dN/dt=1-N/K

Answer

### Step-by-Step Solution:

1. **Understanding the Sigmoid/Logistic Growth Curve**:
- The sigmoid or logistic growth curve is a graphical representation of how a population grows over time when resources are limited. It typically shows four distinct phases: lag phase, exponential phase, deceleration phase, and asymptote phase.

2. **Identifying the Phases**:
- **Lag Phase**: Initially, the population grows slowly as individuals acclimatize to the environment.
- **Exponential Phase**: The population begins to grow rapidly as resources are abundant.
- **Deceleration Phase**: Growth rate slows down as resources become limited.
- **Asymptote Phase**: The population reaches its carrying capacity (K), where growth stabilizes.

3. **Carrying Capacity (K)**:
- The carrying capacity (K) is the maximum population size that an environment can sustain indefinitely without being degraded. In the logistic growth model, this is represented by a horizontal line on the graph.

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

5. **Conclusion**:
- The sigmoid/logistic growth curve is characterized by its S-shape and the presence of the carrying capacity, which indicates the limit of resources available for the population.