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If a Population Growing Exponentially Double in Size in 3 Years, What is the Intrinsic Rate of Increase (R) of the Population - CBSE (Science) Class 12 - Biology

ConceptPopulation Population Attributes

Question

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

Solution

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:

Nt = No ert

Where,

Nt= Population density after time t

NO= Population density at time zero

r = Intrinsic rate of natural increase

= 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:

⇒ log 2 = 3r log e

⇒ log2/(3loge)=r

⇒ log2/(3xx0.434)= r

⇒ 0.301/1.302 = r

⇒ 0.2311 = r

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

Is there an error in this question or solution?

APPEARS IN

NCERT Solution for Biology Textbook for Class 12 (2018 to Current)
Chapter 13: Organisms and Populations
Q: 6 | Page no. 239

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Solution If a Population Growing Exponentially Double in Size in 3 Years, What is the Intrinsic Rate of Increase (R) of the Population Concept: Population - Population Attributes.
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