AdN/dt=rN/N-K/K
BdN/dt= rN(K-N)/K
CdN/dt =rN
DdN/dt= rN/N-K/N
Answer:
B. dN/dt= rN(K-N)/K
Read Explanation:
Logistic Population Growth
The logistic growth model describes population growth that slows down as it reaches the maximum carrying capacity of the environment.
Mathematical Equation: The standard differential equation for logistic growth is represented as: dN/dt = rN(K - N/K).
Key Variables:
dN/dt: The rate of change of population size over time.
r: The intrinsic rate of increase (the per capita rate of growth when resources are unlimited).
N: The current population size.
K: The carrying capacity (the maximum population size that the environment can sustain).
Characteristics of the Model:
Sigmoid Curve: When plotted on a graph with population size (N) against time (t), the result is an S-shaped curve, often referred to as a sigmoid curve.
Phases: The curve typically shows a lag phase (initial slow growth), an exponential phase (rapid growth), and a stationary/plateau phase (growth levels off as it approaches K).
Environmental Resistance: Unlike exponential growth (J-shaped curve), the logistic model accounts for environmental resistance, which includes limiting factors such as food availability, space, competition, and disease.
Significance: This model is widely used in population ecology to understand resource management, conservation biology, and sustainable development planning.