Observe the given population growth formula
`(dN)/(dt)=rN`
Now selecte 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 of these

Answer

To solve the question regarding the population growth formula `(dN)/(dt) = rN`, we will analyze the components of the equation and the implications of the growth model it represents.

### Step-by-Step Solution:

1. **Understanding the Formula**:
The formula `(dN)/(dt) = rN` describes how the population size (N) changes over time (t). Here, `dN/dt` represents the rate of change of the population size, `r` is the intrinsic rate of natural increase (birth rate minus death rate), and `N` is the current population size.

**Hint**: Identify what each component of the formula represents.

2. **Exponential Growth**:
This formula indicates exponential growth. Exponential growth occurs when resources are unlimited, allowing the population to grow without constraints. The population size increases continuously and does not level off.

**Hint**: Consider the conditions under which exponential growth occurs.

3. **Population Size and Growth Rate**:
As the population size (N) increases, the rate of growth (`dN/dt`) also increases because `r` is constant. This means that the larger the population, the more individuals there are to reproduce, leading to a faster growth rate.

**Hint**: Think about how population size affects the growth rate in this model.

4. **Continuous Process**:
The growth described by this formula is continuous, meaning that there are no discrete jumps in population size; it grows smoothly over time.

**Hint**: Reflect on the nature of growth in biological populations.

5. **Identifying the Correct Option**:
Based on the analysis:
- The population growth is indeed exponential.
- The growth rate increases as the population size increases.
- The growth is continuous.
- `r` is constant, while `N` varies.

Therefore, the correct option would be the one that states: "R is constant and N is variable."

### Final Answer:
The correct option is that "R is constant and N is variable."