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.