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

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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?

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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

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:
⇒ log 2 = 3r log e

=> log2/31oge =r

=> log2/ 3x0.434 =r

=> 0.301/1.302 =r

=> 0.2311=r

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