Exponential population growth is:

Options

A. dN/dt=rN
B. dt/dN=rN
C. dN/rN=dt
D. rN/dN = dt

Explanation

**Step-by-Step Text Solution:**

1. **Understanding Exponential Population Growth**: Exponential population growth refers to a situation where the population size increases at a rate proportional to its current size. This means that as the population grows, the number of individuals added to the population also increases.

2. **Formula for Exponential Growth**: The mathematical representation of exponential population growth is given by the formula:
\[ \frac{dn}{dt} = rn \]
Here, \( \frac{dn}{dt} \) represents the rate of change of the population size over time, \( r \) is the intrinsic growth rate, and \( n \) is the current population size.

3. **Breaking Down the Formula**:
- \( \frac{dn}{dt} \): This term indicates how the population size changes over time.
- \( r \): This is the intrinsic growth rate, which reflects how quickly the population can grow under ideal conditions (i.e., unlimited resources).
- \( n \): This represents the current number of individuals in the population.

4. **Conclusion**: Therefore, exponential population growth occurs when the population grows continuously and rapidly, leading to a J-shaped growth curve when plotted over time. The correct answer to the question is option (a), which states that exponential population growth is represented by the equation \( \frac{dn}{dt} = rn \).

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