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.