Answer

Example : Elongation of root at a constant rate. When a graph is drawn of length against time ; linear curve is obtained.

Mathematically its expression is given below :

L_{t} = L_{0}+rt

Here, L_{t} is length at time ‘t’, L_{0} is length at time 0 and r is the rate per unit time.

**(b) Geometric growth : **In this type of growth the initial growth is slow and is called the lag phase. After this, the growth is quite rapid and at an exponential rate. This phase is called the log or exponential phase. In this phase, both the daughter cells (formed after mitosis) continue to divide. The last phase marks a slowed down growth. This happens because of limited nutrient supply. This phase is called the stationary phase. The graph of the geometric growth gives a sigmoid curve.

The exponential growth can be mathematically represented as follows:

W_{1} = W_{0}ert

Here, W1 = final size (weight, height, number etc.), W0 = initial size at the beginning of the period, r = growth rate, t = time of growth and e = base of natural logarithms

**(c) Sigmoid growth curve : **The S-shaped curve on graph; to show geometric growth is called the sigmoid growth curve. It is S shaped curve which is characteristic feature of living organism in natural environment. It consists of lag phase, log phase or exponential phase and stationary phase.

**(d) Absolute and relative growth rates**

Absolute growth rate : It is the measurement and comparison of total growth per unit time. When growth is measured in absolute terms, e.g. in terms of length or weight, it is called absolute growth.

Relative growth rate : It is the growth of given system per unit time expressed on common basis eg per unit initial parameter is relative growth rate. When growth is measure in terms of comparative terms; like percentage growth; it is called relative growth.

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