Go through the population growth formula
`(dN)/(dt)=rN`
Now select the correct option -

Options

A. As population gets larger, its rate of growth increases
B. Represents growth as a continuous process
C. r is constant and N is variable
D. All

Answer

To solve the question regarding the population growth formula \( \frac{dN}{dt} = rN \), we will analyze the components of the equation and the implications of each part.

### Step-by-Step Solution:

1. **Understanding the Formula**:
- The formula \( \frac{dN}{dt} = rN \) describes how a population (N) changes over time (t).
- Here, \( \frac{dN}{dt} \) represents the rate of change of the population size.
- \( r \) is the intrinsic rate of natural increase (growth rate), which is constant in this model.
- \( N \) is the current population size.

2. **Interpreting the Variables**:
- As the population size \( N \) increases, the term \( rN \) indicates that the rate of change of the population size increases.
- This means that larger populations grow more rapidly than smaller ones, leading to exponential growth.

3. **Exponential Growth**:
- The equation represents exponential growth, which is characterized by a J-shaped curve when graphed.
- In this model, there are no lag or log phases; growth is continuous and accelerates as the population size increases.

4. **Key Points**:
- \( r \) is constant, meaning the growth rate does not change with population size.
- \( N \) is variable, indicating that the population size can change over time.
- The growth is continuous, meaning there are no interruptions or phases in the growth process.

5. **Selecting the Correct Option**:
- Based on the analysis, the correct option is option 4, which states that \( \frac{dN}{dt} = rN \) leads to an exponential growth curve.

### Summary:
The population growth formula \( \frac{dN}{dt} = rN \) indicates that as the population size increases, the growth rate also increases, leading to exponential growth. The correct option is option 4.