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'r' represents Intrinsic rate of natural increase.
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Read the following text and answer the following question on the basi...
Understanding the Population Growth Equation
The equation provided, dN/dt = rN(K-N)/K, is a model used in ecology to describe population growth over time. Each component of this equation has a specific meaning, and understanding these will clarify why 'r' represents the intrinsic rate of natural increase.
Components of the Equation
- dN/dt: This term indicates the change in population size (N) over time (t).
- N: Represents the current population size.
- K: Denotes the carrying capacity of the environment, which is the maximum population size that the environment can sustain.
Role of 'r' in Population Growth
- Definition of 'r': In this equation, 'r' specifically refers to the intrinsic rate of natural increase. This is a measure of how quickly a population can grow under ideal conditions, where resources are abundant and environmental pressures are minimal.
- Impact of 'r':
- If 'r' is high, the population can grow rapidly, as there are fewer limitations on its growth.
- Conversely, if 'r' is low, the population growth will be slower.
Why 'r' is Option B
- Option A (Population density at time Y): This does not define 'r'.
- Option C (Carrying capacity): This refers to 'K', not 'r'.
- Option D (The base of natural logarithm): This is unrelated to population growth.
Thus, option B correctly identifies 'r' as the intrinsic rate of natural increase, making it the correct answer in the context of the population growth equation.
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