A population growing in a habitat with limited resources shows four phases of growth in the following sequence:

Options

A. Acceleration-deceleration-lag phase-asymptote
B. Asymptote-acceleration-deceleration -lag phase
C. Lag phase-accceleration-deceleration -asymptote
D. Acceleration -lag phase-deceleration -asymptote

Answer

To answer the question regarding the four phases of growth in a population growing in a habitat with limited resources, we can break down the solution step by step:

### Step-by-Step Solution:

1. **Understanding Population Growth**:
- A population growing in a habitat with limited resources will experience different phases of growth due to the availability of resources and environmental factors.

2. **Identifying the Phases of Growth**:
- The four phases of growth in such a population can be identified as:
- **Lag Phase**: This is the initial phase where the population is small, and growth is slow as individuals acclimatize to the environment. Resources are not fully utilized.
- **Exponential Growth Phase (Acceleration)**: After the lag phase, the population begins to grow rapidly as resources become more available. This phase is characterized by a sharp increase in population size.
- **Deceleration Phase**: As the population continues to grow, resources start to become limited. The growth rate begins to slow down as competition for resources increases.
- **Asymptotic Phase**: Finally, the population reaches its carrying capacity (denoted as K), where the growth rate levels off and stabilizes. The population size remains relatively constant as it oscillates around the carrying capacity.

3. **Graphical Representation**:
- The growth can be represented graphically as a sigmoid (S-shaped) curve. Initially, the curve rises slowly (lag phase), then steeply (exponential growth), followed by a gradual flattening (deceleration), and finally leveling off (asymptotic phase).

4. **Mathematical Representation**:
- The growth can be described using the logistic growth equation:
\[ \frac{dn}{dt} = rN \left( \frac{K - N}{K} \right) \]
where:
- \(N\) = population density at a given time,
- \(K\) = carrying capacity of the environment,
- \(r\) = intrinsic rate of natural increase.

5. **Conclusion**:
- The correct sequence of growth phases for a population in a habitat with limited resources is: **Lag Phase → Exponential Growth (Acceleration) → Deceleration → Asymptotic Phase**.