Question:

The exponential growth can be expressed $ w_{t}=w_{0}e^{rt} $ whereas $e$ denotes

Updated On: Aug 15, 2022
  • growth rate
  • time of growth
  • base of nature logarithm
  • final size
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The Correct Option is C

Solution and Explanation

Population growth curve are the mathematical expression of the growth of a population, which are used to predict the growth rate of population from its beginning till its climax stage i.e., stability. These growth curve may be $S$-shaped or sigmoid shape or $J$-shaped. The later $J$-shaped curve is shown by small population and contain two phases e.g., lag phase and exponential phase and is represented by following exponential equation $ \frac{dN}{dt}=rN $ Where, $r$ denote intrinsic rate of natural increases and $N$ is size of population, while $dN/dt$ is rate of change in population size. The integral form of the above reaction can be derived as $ W_{t}=W_{0}\,e^{n} $ where, $ W_{t}= $ population density after time $t$ $ W_{O}= $ population density at time $0$ $e$ = the base of natural logarithm $r =$ intrinsic rate of natural increase.
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Concepts Used:

Organisms and Populations

Organisms:

An attached living system that lives in an environment is commonly known as an organism. These organisms are able to retain certain behaviors and structures. Some examples of organisms are plants, animals, bacteria, fungi, and humans. A group of these organisms leads to the formation of a population. The collection of the population forms a community that assists in the operation of ecosystems. 

Each and every organism has the ability to adapt itself to various conditions of the environment. This capacity of organisms is due to their genetic variations. It is due to this only that their probability of survival get increases. For instance, camels adapt themselves to survive in desert areas and polar bears adapt to the extreme cold conditions or situations through their dense fur coat.

Populations:

A collection of organisms or individuals of a species that live, at a specific time, in a geographical area that is well-defined and capable of interbreeding is described as a population.

Read More: Organisms and Populations