Given below is an equation describing the growth pattern of a population :
\( \dfrac{dN}{dt} = rN \)
(a) Mention the type of growth model or growth pattern of the population described by the given equation.
(b) What does r in the equation signify ?
(c) Mention the type of growth curve that will be obtained if the population density (N) is plotted against time (t).
(d) According to you, will the resource availability be limited or unlimited for this type of growth in the given population ?
Given below is an equation describing the growth pattern of a population :
\( \dfrac{dN}{dt} = rN \)
(a) Mention the type of growth model or growth pattern of the population described by the given equation.
(b) What does r in the equation signify ?
(c) Mention the type of growth curve that will be obtained if the population density (N) is plotted against time (t).
(d) According to you, will the resource availability be limited or unlimited for this type of growth in the given population ?
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Solution and Explanation
The equation \( \dfrac{dN}{dt} = rN \) says that the rate of change of population size is directly proportional to the number of individuals present.
Here N is the population density, t is time and r is a constant.
Step 2: (a) Type of growth:
This is the exponential growth model. The population grows faster and faster as N becomes larger.
Step 3: (b) Meaning of r:
r is the intrinsic rate of natural increase of the population.
It is the difference between the birth rate and the death rate per individual (\( r = b - d \)).
Step 4: (c) Shape of the curve:
When N is plotted against t the curve is J-shaped, because the growth first looks slow and then rises steeply.
Step 5: (d) Resources:
Resources such as food and space are unlimited. Only then can every individual breed at its full rate without competition.
Final Answer:
(a) Exponential growth. (b) r is the intrinsic rate of natural increase. (c) J-shaped curve. (d) Resources are unlimited.
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