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The equation for J-shaped population gro...

The equation for J-shaped population growth curve is

A

`(dN)/(dt)=rN`

B

`(dN)/(dt)=rN ((K-N)/K)`

C

`N_t=N_0+B+I-D-E`

D

`D=N/S`

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The correct Answer is:
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: \[ \frac{dn}{dt} = rN \]
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