Question

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

Answer 1

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.