(a) Arithmetic growth: In arithmetic growth, following mitotic cell division, only one daughter cell continues to divide while the other differentiates and matures. A root elongating at a constant rate exemplifies the simplest expression of arithmetic growth. On plotting the length of the organ against time, a linear curve is obtained. Mathematically, it is expressed as – L_t = L₀+ rt L_t = length at time ‘t’ L₀ = length at time ‘0’ r = growth rate / elongation per unit time. (b) Geometric 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 a mitotic cell division retain the ability to divide and continue to do so. However, with a limited nutrient supply, the growth solws down leading to a stationary phase. If we plot the parameter of growth against time, we get a typical sigmoid or S- curve. An S- shaped curve is a characteristic of the living organism growing in a natural environment. The exponential growth can be expressed as W₁ = W₀e^rt W₁ = final size (weight, height, number etc) W₀ = 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 rate and is also the measure of the ability of the plant to produce new plant material, referred to as efficiency index. Hence, final size of W₁ depends on the initial size, W₀. Arithmetic growth Geometric growth Stages during development showing geometric and arithmetic phase.    (c) Sigmoid growth curve. When the rate of growth of a cell, organ or an entire plant is plotted against time, an S- shaped curve, called the sigmoid curve is obtained. It shapes lag phase, log (exponential) phase, diminishing phase and stationary phase. The rate of growth varies in different species and in different organs. Growth begins slowly, and then enters a period of rapid enlargement, following which it gradually decreases, till no further enlargement. The mathematical curve, which represents this variation in growth rate, is ‘S’ – shaped or sigmoid growth curve. Three phases of growth curve 1. Lag phase – phase of cell division. 2. Exponential phase (Log Phase) - phase of cell elongation 3. Stationary phase (steady phase) - phase of cell maturation. (d) Absolute and relative growth rate. Quantitative comparisons between the growth of living systems can be made in two ways : (i) measurement and the comparison of total growth per unit time is called the absolute growth rate. (ii) The growth of the given system per unit time expressed on a common basis e.g. per unit initial parameter is called the relative growth rate.