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Organisms And Populations

Question
CBSEENBI12001085

If the population growing exponentially doubles in size in 3 years, what is the intrinsic rate of increase (r) of the population?

Solution

The exponential growth can be calculated by the following integral form of the exponential growth equation:

Nt = No ert

Where,

Nt= Population density after time t

NO= Population density at time zero

r = Intrinsic rate of natural increase

e = Base of natural logarithms (2.71828)

Now, as per the question,

Present population density = x

Then, Population density after two years = 2x

t = 3 years

Substituting these values into the formula, we get:

⇒ 2x = x e3r

⇒ 2 = e3r

Applying log on both sides:

⇒ log 2 = 3r log e
rightwards double arrow space fraction numerator log space 2 space over denominator 3 space log space straight e end fraction space equals space straight r
rightwards double arrow space fraction numerator log space 2 over denominator 3 space straight x space 0.434 end fraction space equals space straight r
rightwards double arrow fraction numerator 0.301 over denominator 3 space straight x space 0.434 end fraction space equals space straight r
rightwards double arrow space fraction numerator 0.301 over denominator 1.302 end fraction space equals space straight r
rightwards double arrow space 0.2311 space equals space straight r

Hence, the intrinsic rate of increase for the above-illustrated population is 0.2311.

Some More Questions From Organisms and Populations Chapter

In which interaction only one species is benefitted while the other species is neither harmed nor benefitted ?

Which of the following interaction both species suffer ?

In which of the following interaction both species are benefitted ?

Fill in the blanks with suitable words :

1. The optimal capacity of the organism to produce offspring is called........................

2. Rapid increase in human population is called........................

3. Mathematical expression of the growth of population is called........................

4. Yeast cells grown in a culture medium show........................growth curve.

5. Main cause of population explosion is........................

State true or false :

Coin one word for the following statements :

1.Organism that can tolerate only a narrow range of salinity.

2. Plants that can survive a wide range of temperature.

3. Interaction of two species in which one is benefited while other is neither benefited nor harmed.

4. Number of births during a given period in the population that are added to the initial density.

5. the process of maintaing a constant body temperature.

A few organisms can tolerate and thrive in a wide range of temperature, they are called........................

Majority of organisms are restricted to a narrow range of temperature, such organisms are called ........................ 

The organisms ideally try to maintain the constancy of its internal environment by the process called........................

Mammals from colder climates have shorter ears and limbs to minimize heat loss. This rule is called........................