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 sufficient amounts of food resources are available to the individual. Its exponential growth can be calculated by the following integral form of the exponential growth 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 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 e^3r

⇒ 2 = e^3r

Applying log on both sides:

⇒ log 2 = 3r log e

⇒ `log2/(3loge)=r`

⇒ `log2/(3xx0.434)= r`

⇒ `0.301/1.302 = r`

⇒ 0.2311 = r

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