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 = No rt
Where,
Nt Population density after lime 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 = x e3r
⇒2 = e3r
Applying log on both sides:
⇒ log2 = 3r loge
$\frac{log 2}{3loge} = r$
$\frac{log 2}{3x0.434} = r$
$\frac{0. 301}{3x0.434} =r$
$\frac{0.301}{1.302}=r$
$⇒ 0. 2311=r$
Hence the intrinsic rate of increase for the above illustrated population is 0. 2311.