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

Apopulation grows exponentially if sufficient amounts of foodresources are available to the individual. Its exponential growth canbe calculated by the following integral form of the exponentialgrowth equation:

N_t= N_o e^rt

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 theabove equation, we can calculate the intrinsic rate of increase (r)of a population.

Now, asper the question,

Presentpopulation density = x

Then,

Populationdensity after two years = 2x

t = 3years

Substitutingthese values in the formula, we get:

⇒2x = x e^3r

⇒2 = e^3r

Applyinglog on both sides:

⇒log 2 = 3r log e

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