What is meant by growth models?

(A) $\Rightarrow$ Growth models represent the specific and predictable patterns of population growth over time.
Population growth occurs based on the availability of food, habitat conditions, and the presence of other biotic and abiotic factors.
There are two main types of models:
$(a)$ Exponential Growth: This type of growth occurs when food and space are available in sufficient amounts.
When resources in the habitat are unlimited, each species has the ability to realize its innate potential to grow in number fully.
- The population grows in an exponential or geometric fashion.
If in a population of size $N$, the birth rate is represented as '$b$' and the death rate as '$d$'.
$\Rightarrow$ Then the increase or decrease in $N$ during a unit time period '$t$' will be $dN/dt = (b-d) \times N$.
Let $(b-d) = r$, then $dN/dt = rN$.
Here, '$r$' is called the 'intrinsic rate of natural increase' and is a very important parameter for assessing the impacts of any biotic or abiotic factor on population growth.
To provide an idea of the magnitude of '$r$' values: for the Norway rat, '$r$' is $0.015$, and for the flour beetle, it is $0.12$.
In $1981$, the '$r$' value for the human population in India was $0.0205$.
The above equation describes the exponential or geometric growth pattern of a population and results in a $J$-shaped curve when $N$ is plotted in relation to time.
Using basic calculus, the integral form of the exponential growth equation is $N_t = N_0 e^{rt}$.
Where $N_t = \text{Population density after time } t$, $N_0 = \text{Population density at time zero}$, $r = \text{intrinsic rate of natural increase}$, and $e = \text{the base of natural logarithms } (2.71828)$.
Any species growing exponentially under unlimited resource conditions can reach enormous population densities in a short time.
Darwin showed how even a slow-growing animal like an elephant could reach enormous numbers in the absence of checks.
$(b)$ Logistic Growth: No population of any species in nature has unlimited resources at its disposal to permit exponential growth.
This leads to competition between individuals for limited resources. Eventually, the 'fittest' individual will survive and reproduce.
Many governments have realized this fact and introduced various restraints to limit human population growth.
In nature, a given habitat has enough resources to support a maximum possible number, beyond which no further growth is possible.