A plot of dN/dt as a function of population density yields as
Rectangular hyperbola.
Negative exponential curve.
Positive rectilinear curve.
Bell-shaped curve.
In certain cases, the relationship between population density and the rate of change of population size can follow a pattern known as the logistic growth model. Initially, when the population density is low, the population experiences exponential growth, resulting in an increasing rate of change (dN/dt). However, as the population approaches its carrying capacity (the maximum number of individuals the environment can support), the growth rate starts to slow down and eventually levels off.
At the carrying capacity, the rate of change of population size becomes zero as the birth rate and death rate balance each other out. This point corresponds to the peak of the bell-shaped curve. The curve represents the sigmoidal growth pattern exhibited by populations following the logistic growth model.
So, the correct answer is option 4 which is a bell-shaped curve.