Which of the following statements is correct ?

Options

A. Geometric growth produces J-shaped population growth curve.
B. Logistic growth occurs when resources are limiting.
C. Equation for exponential growth is `N_(t) = N_(0)e^(rt)`
D. All of these

Answer

To determine which of the statements regarding population growth models is correct, we will analyze each statement step by step.

### Step 1: Understanding Geometric Growth
The first statement claims that geometric growth produces a J-shaped population growth curve.

- **Explanation**: Geometric growth, also known as exponential growth, occurs when a population has unlimited resources. In this scenario, the population grows rapidly without any constraints, leading to a J-shaped curve when plotted on a graph with population density (n) on the y-axis and time (t) on the x-axis.

### Step 2: Understanding Logistic Growth
The second statement mentions that logistic growth occurs when resources are limiting.

- **Explanation**: Logistic growth is a more realistic model of population growth. It occurs when resources are limited, leading to competition among individuals. This model introduces the concept of carrying capacity (K), which is the maximum population size that an environment can sustain. When plotted, logistic growth results in an S-shaped (sigmoid) curve, indicating that the population grows rapidly at first but slows as it approaches the carrying capacity.

### Step 3: Analyzing the Exponential Growth Equation
The third statement provides the equation for exponential growth: \( n_T = n_0 e^{rT} \).

- **Explanation**: In this equation:
- \( n_T \) is the final population after time \( T \).
- \( n_0 \) is the initial population size.
- \( e \) is the base of the natural logarithm.
- \( r \) is the intrinsic rate of natural increase.
- This equation correctly represents exponential growth, where the carrying capacity (K) is not considered since resources are unlimited.

### Conclusion
After analyzing all three statements:
- Statement A is correct: Geometric growth produces a J-shaped curve.
- Statement B is correct: Logistic growth occurs when resources are limiting.
- Statement C is correct: The equation for exponential growth is accurately stated.

Thus, the correct answer is **Option D: All of these statements are correct**.

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