Q. 64.0( 6 Votes )

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

Answer :

When resources are unlimited, populations exhibit exponential growth, resulting in a J-shaped curve. Its exponential growth can be calculated by the following equation:

Where,

N_{t} = Population density after time t

N_{o} = 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:

Applying log on both sides:

⇒ log 2 = 3r log e

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

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