Which of the following statements are true regarding the exponential growth model of a population?
I. Exponential growth model shows a S-shaped growth curve.
II. Exponential growth curve is expressed by the equation dN/dt = rN.
III. Any species growing exponentially under unlimited resources can reach enormous population densities in a short time.
Which of the following statements are true regarding the exponential growth model of a population?
I. Exponential growth model shows a S-shaped growth curve.
II. Exponential growth curve is expressed by the equation dN/dt = rN.
III. Any species growing exponentially under unlimited resources can reach enormous population densities in a short time.
The correct option is C II and III
In exponential growth, the population size increases at an exponential rate (a steady increase in quantity over time). In this growth model, the population growth in a particular habitat depends only on the number of individuals available to reproduce, as the availability of resources are unlimited (food, shelter etc.).
This exponential growth model results in a ‘J’ - shaped growth curve, when population density (N) is plotted in relation to time ‘t’. Population density is the number of people per unit of area (per square kilometre). So statement I is false.
In the exponential growth model, the curve representing rate of change of population density is represented as
dN/dt = rN
where,
dN represents the change in the population density
dt represents the change in time ‘t’
r represents the intrinsic rate of natural increase. It is the difference between the birth rate and death rate in a population.
Thus statement II is true.
Any species growing exponentially under unlimited resources can reach enormous population densities in a short time. But this is an unrealistic situation. In nature exponential growth may not be possible due to various factors like competition, scarcity of nutrients, environmental stress etc. As per exponential growth model a slow growing animal like an elephant could grow exponentially in the absence of checks. Hence statement III is true.
In exponential growth, the population size increases at an exponential rate (a steady increase in quantity over time). In this growth model, the population growth in a particular habitat depends only on the number of individuals available to reproduce, as the availability of resources are unlimited (food, shelter etc.).
This exponential growth model results in a ‘J’ - shaped growth curve, when population density (N) is plotted in relation to time ‘t’. Population density is the number of people per unit of area (per square kilometre). So statement I is false.
In the exponential growth model, the curve representing rate of change of population density is represented as
dN/dt = rN
where,
dN represents the change in the population density
dt represents the change in time ‘t’
r represents the intrinsic rate of natural increase. It is the difference between the birth rate and death rate in a population.
Thus statement II is true.
Any species growing exponentially under unlimited resources can reach enormous population densities in a short time. But this is an unrealistic situation. In nature exponential growth may not be possible due to various factors like competition, scarcity of nutrients, environmental stress etc. As per exponential growth model a slow growing animal like an elephant could grow exponentially in the absence of checks. Hence statement III is true.
