If there are sufficient amounts of food resources available to an individual population, it will grow exponentially. The exponential growth equation can be expressed as the following integral form:

Where,

N 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=xe3r

=2=e3r

Applying log on both sides:

⇒log 2 =3rloge

log2/ 3 loge=r

log 2 /3x0.434 =r

0.301

3×0.434

=0.301/1.302

=r =0.2311=r

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