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.
Top Questions on Organisms and Populations
- Read the following passage and answer the questions that follow:
In nature, we rarely find isolated, single individuals of any species; majority of them live in groups in a well-defined geographical area, share or compete for similar resources, potentially interbreed and thus constitute a population. The population has certain attributes whereas, an individual organism does not. A population at a given time is composed of individuals of different ages. The size of the population tells us a lot about its status in the habitat. Whatever ecological processes we wish to investigate in a population, be it the outcome of competition with another species, the impact of the predator or the effect of pesticide application, we always evaluate in terms of any change in the population size. The size, in nature, could be low or go into millions. Population size, technically called population density (N) need not necessarily be measured in numbers only. The size of a population for any species is not a static parameter. It keeps on changing with time depending on various factors including food availability, predation pressure and adverse weather. (a) The Monarch butterfly is highly distasteful to its predator because of a special chemical present in its body. How does the butterfly acquire this chemical?
(b) If population density at a time t + 1 is 800, Emigration = 100, Immigration = 200, Natality = 200 and Mortality = 150, calculate the population density at time t and comment upon the type of age pyramid that will be formed in this case.
Student to attempt either sub-part (c) or (d):
(c) What is the difference in a method of measuring population density in an area if there are 200 carrot grass plants to only single huge banyan tree?
\begin{center} OR \end{center} (d) Name two methods to measure the population density of tigers.- CBSE CLASS XII - 2025
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Applications were received for 1,50,000 equity shares and allotment was made to the applicants as follows:
Category A: Applicants for 90,000 shares were allotted 70,000 shares.
Category B: Applicants for 60,000 shares were allotted 30,000 shares.
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Pass necessary journal entries for the above transactions in the books of Alexia Limited. Open calls in arrears and calls in advance account, wherever necessary.
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