Exponential population growth is

Options

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

Answer

### Step-by-Step Solution

1. **Understanding Exponential Population Growth**:
Exponential population growth occurs when a population increases in size at a rate proportional to its current size. This typically happens when resources are unlimited, allowing for continuous reproduction without constraints.

2. **Identifying the Formula**:
The mathematical representation of exponential growth is given by the equation:
\[ \frac{dN}{dt} = rN \]
where:
- \( \frac{dN}{dt} \) is the rate of change of the population size over time,
- \( r \) is the intrinsic growth rate,
- \( N \) is the current population size.

3. **Analyzing the Options**:
- Option A: \( \frac{dN}{dt} = rN \) (Correct)
- Option B: \( \frac{dt}{dN} \) (Incorrect)
- Option C: \( \frac{dN}{rN} \) (Incorrect)
- Option D: \( \frac{r}{N} \frac{dN}{dt} \) (Incorrect)

4. **Conclusion**:
The correct option that represents exponential population growth is:
\[ \frac{dN}{dt} = rN \]
Therefore, the answer is **Option A**.