The equation for J-shaped population growth curve is

Options

A. `(dN)/(dt)=rN`
B. `(dN)/(dt)=rN ((K-N)/K)`
C. `N_t=N_0+B+I-D-E`
D. `D=N/S`

Answer

To determine the equation for the J-shaped population growth curve, we need to understand the characteristics of this type of growth. The J-shaped growth curve is typically associated with exponential growth, where resources are unlimited, allowing a population to grow rapidly after an initial period of slow growth.

### Step-by-Step Solution:

1. **Understand the Growth Models**:
- There are two main growth models: exponential growth and logistic growth. The J-shaped curve corresponds to exponential growth.

2. **Identify Conditions for Exponential Growth**:
- Exponential growth occurs when resources such as food, space, and water are unlimited. Under these conditions, a population can grow rapidly.

3. **Recognize the Initial Growth Phase**:
- Initially, the population grows slowly as it adapts to environmental conditions. After this adaptation phase, the population begins to grow exponentially.

4. **Write the Equation**:
- The mathematical representation of exponential growth is given by the equation:
\[ \frac{dn}{dt} = rN \]
- Here:
- \(\frac{dn}{dt}\) represents the rate of population growth.
- \(r\) is the intrinsic rate of natural increase.
- \(N\) is the current population density.

5. **Conclusion**:
- Therefore, the equation for the J-shaped population growth curve is:
\[ \frac{dn}{dt} = rN \]