Class 12 Biology - Chapter Organisms and Population NCERT Solutions | If a population growing exponentially do
If a population growing exponentially double in size in 3 years, what is the intrinsic rate of increase (r) of the population?
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:
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
Hence, the intrinsic rate of increase for the above illustrated population is 0.2311.
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7 Comment(s) on this Question
Thank you so much
Thank youð
It's value of e not of loge 0.434 is nothing but value of loge
Sir can u tell me log e value is 2.7 nd log 3 is 0.4 bt here 3 * 0.434 why?
Thanks a lot ð
yupp i did the same...
The ârâis the specific growth rate ( dN/Ndt ) when population growth is exponential. ( Population becomes 2 from 1 in three years. dN= 2, N=1 and dt = 3 ) By putting the values we get 2/ 1x3 = 0.66, it is so simple
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