Explain exponential growth as a growth model with a suitable graph and examples.

(N/A) For the unimpeded growth of a population,the availability of resources (food and space) is essential. Ideally,when resources in the habitat are unlimited,each species has the ability to realize fully its innate potential to grow in number,as Darwin observed while developing his theory of natural selection. In such conditions,the population grows in an exponential or geometric fashion.
If in a population of size $N$,the birth rates (not total number but per capita births) are represented as $b$ and death rates (per capita deaths) as $d$,then the increase or decrease in $N$ during a unit time period $t$ $(dN/dt)$ will be:
$dN/dt = (b - d) \times N$
Let $(b - d) = r$,then:
$dN/dt = rN$
The $r$ in this equation is called the 'intrinsic rate of natural increase' and is a very important parameter chosen for assessing impacts of any biotic or abiotic factor on population growth.
To give you some idea about the magnitude of $r$ values,for the Norway rat,the $r$ is $0.015$,and for the flour beetle,it is $0.12$. In $1981$,the $r$ value for the human population in India was $0.0205$.