If a population growing exponentially double in size in 3 years what is the intrinsic rate of increase (r) of the population?
Solution and Explanation
A population grows exponentially if sufficient amounts of food resources are available to the individual. Its exponential growth can be calculated by the following integral form of the exponential growth equation:
N = No rt
Where,
Nt Population density after lime t
No Population density at time zero
r = Intrinsic rate of natural increase
e = Base of natural logarithms (2. 71828)
From the above equation we can calculate the intrinsic rate of increase (r) of a population.
Now as per the question
Present population density = x
Then
Population density after two years = 2x
t = 3 years
Substituting these values in the formula we get:
⇒ 2x = x e3r
⇒2 = e3r
Applying log on both sides:
⇒ log2 = 3r loge
\(\frac{log 2}{3loge} = r\)
\(\frac{log 2}{3x0.434} = r\)
\(\frac{0. 301}{3x0.434} =r\)
\(\frac{0.301}{1.302}=r\)
\(⇒ 0. 2311=r\)
Hence the intrinsic rate of increase for the above illustrated population is 0. 2311.
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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.
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