Choose the correct option -

Options

A. Geometric growth produces J-shaped population growth curve
B. Logistic growth occurs when resources are limiting
C. For exponential growth equation is `N_t=N_0e^(rt)`
D. All

Answer

To solve the question, we need to evaluate each option provided and determine if they are correct statements regarding population growth.

### Step-by-Step Solution:

1. **Evaluate Option 1: Geometric growth produces a J-shaped population growth curve.**
- Geometric growth indeed produces a J-shaped curve, which represents the rapid increase in population size under ideal conditions. This growth is characterized by three phases: lag phase (slow growth), exponential growth phase (rapid growth), and stationary phase (slow growth again).
- **Conclusion:** This option is correct.

2. **Evaluate Option 2: Logistic growth occurs when resources are limited.**
- Logistic growth is a model that describes how a population grows more slowly as it approaches its carrying capacity due to limited resources. This is often illustrated by an S-shaped curve. The concept of "survival of the fittest" applies here as individuals compete for limited resources.
- **Conclusion:** This option is also correct.

3. **Evaluate Option 3: The exponential growth equation is nt = n0 * e^(rt).**
- The equation for exponential growth is indeed represented as \( N_t = N_0 \cdot e^{rt} \), where \( N_t \) is the population at time \( t \), \( N_0 \) is the initial population size, \( r \) is the intrinsic rate of natural increase, and \( t \) is time. The statement in the option is slightly misleading as it mentions \( n \) instead of \( N_0 \) for the initial population, but the essence of the equation is correct.
- **Conclusion:** This option is correct despite the minor notation issue.

4. **Evaluate Option 4: All of the above.**
- Since all previous options (1, 2, and 3) have been determined to be correct, this option must also be correct.
- **Conclusion:** This option is correct.

### Final Answer:
The correct answer is **Option 4: All of the above.**

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