Question

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

Answer 1

A population grows exponentially if enough food resources are available to the individual.

Exponential growth equation:

$N_t$= $N_o$ $e^{rt}$

Where,

$N_t$= Population density after time t

$N_t$= 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

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