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

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

Concept: Population - Population Attributes
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#### APPEARS IN

NCERT Class 12 Biology
Chapter 13 Organisms and Populations
Q 6 | Page 239