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प्रश्न
If a population growing exponentially double in size in 3 years, what is the intrinsic rate of increase (r) of the population?
उत्तर
A population grows exponentially if sufficient amounts of food resources are available to the individual. The following integral form of the exponential growth equation can calculate its exponential growth:
Nt = No ert
Where,
Nt = Population density after time 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:
⇒ 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.
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