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**Answer the following question.**

Compare, giving reasons, the J-shaped and S-shaped models of population growth of a species.

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#### Solution

**There are 2 models of population growth:****(i)** The exponential growth**(ii)** Logistic growth

**(i) Exponential growth:**

This growth occurs where the resources (food + space) are unlimited. The equation can be represented as

`(d"N")/(d"t")` = ( b - d ) x N

Let ( b - d ) = r

`(d"N")/(d"t")` = rN or N_{t} = N_{0}e^{rt}

N = population size

N_{t} = population density after time t.

N_{0 }= population density at time zero

r = growth rate

b =birth rate

d = death rate

In this growth, when N in relation to time is plotted on the graph, the curve becomes J-shaped.

**(ii) Logistics growth model: **

This is a realistic approach as the resources become limited at a certain point of time.

**(a) **J-shaped curve ⇒ exponential growth**(b)** S-shaped curve ⇒ logistics growth

Every ecosystem has limited resources to support a particular maximum carrying capacity (K).

When N is plotted in relation to time t, a sigmoid-S-shaped curve is obtained & is also called as VERHULST-PEARL logistic growth.

The equation is:

`(d"N")/(d"t") = "rN" (("K" - "N"))/("K")`

N = population density at time t.

R = growth rate

K = carrying capacity.