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Organisms and Populations — BIOLOGY STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceBIOLOGYOrganisms and Populations4 Marks
Question
Explain exponential growth equation with well labeled diagram.###Explain exponential growth.
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Answer

→ Resource (food and space) availability is obviously essential for the growth of a population.
→ Ideally, when resources in the habitat are unlimited, each species has the ability to realise fully its innate potential to grow in number, as Darwin observed while developing his theory of natural selection.
→ Then the population grows in an exponential or geometric fashion.
→ If in a population of size N, the birth rates (not total number but per capita births) are represented as band death rates (again, per capita death rates) as d, then the increase or decrease in N during a unit time period t
(dN/dt) will be
dN/dt = (b - d) × N
Let (b - d) = r,
Then dN/dt=rN
→ The r in this equation is called the 'intrinsic rate of natural 'increase' and is a very important parameter chosen for assessing impacts of any. biotic or abiotic factor on population growth.
→ The above equation describes the exponential or geometric growth pattern of a population and results in a J-shaped curve when we plot N in relation to time.
Image
→ The integral form of the exponential growth equation as $Nt = N _0 e ^{ rt }$
Image
Where $N_t$ Population density after time t
$N _0$ = Population density at time zero
r = intrinsic rate of natural increase
e = the base of natural logarithms (2.71828)
→ Any species growing exponentially under unlimited resource conditions can reach enormous population densities in a short time.
→ Darwin showed how even a slow growing animal like elephant could reach enormous numbers in the absence of checks.
→ The following is an anecdote popularly narrated to demonstrate dramatically how fast a huge population could build up when growing exponentially.
→ r values, for the Norway rat the r is 0.015, and for the flour beetle it is 0.12.
→ In 1981, the r value for human population in India was 0.0205 and in 2011 r = 0.0135

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