. . Growth Rates The increased growth per unit time is termed as growth rate. Thus, rate of growth can be expressed mathematically.
An organism, or a part of the organism can produce more cells in a variety of ways. Figure13. Diagrammatic representation of : (a) Arithmetic (b) Geometric growth and (c) Stages during embryo development showing geometric and arithematic phases The growth rate shows an increase that may be arithmetic or geometrical (Figure . ).
In arithmetic growth, following mitotic cell division, only one daughter cell continues to divide while the other differentiates and matures. The simplest expression of arithmetic growth is exemplified by a root elongating at a constant rate. Look at Figure . .
On plotting the length of the organ against time, a linear curve is obtained. Mathematically, it is expressed as L t = L + rt L t = length at time ‘t’ L = length at time ‘zero’ r = growth rate / elongation per unit time. Let us now see what happens in geometrical growth. In most systems, the initial growth is slow (lag phase), and it increases rapidly thereafter – at an exponential rate (log or exponential phase).
Here, both the progeny cells following mitotic cell division retain the ability to divide and continue to do so. However, with limited nutrient supply, the growth slows down leading to a stationary phase. If we plot the parameter of growth against time, we get a typical sigmoid or S-curve (Figure . ).
A sigmoid curve is a characteristic of living organism growing in a natural environment. It is typical for all cells, tissues and organs of a plant. Can you think of more similar examples? What kind of a curve can you expect in a tree showing seasonal activities?
The exponential growth can be expressed as W = W e rt W = final size (weight, height, number etc.) W = initial size at the beginning of the period r = growth rate t = time of growth e = base of natural logarithms Here, r is the relative growth