**Q.3:- Describe briefly:**

**(a) Arithmetic growth**

**(b) Geometric growth**

**(c) Sigmoid growth curve**

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

**Answer:- **

(a) Arithmetic growth: If the length of a plant organ is plotted against time it shows a linear curve, the growth is called arithmetic growth. In this growth, the rate of growth is constant and increase in growth occurs in arithmetic progression e.g., length of a plant is measured as 2,4, 6, 8,10,12 cms at a definite interval of 24 hrs. It is found in root or shoot elongating at constant rate. Arithmetic growth is expressed as L_{t} = L_{0} + r_{t }Here, L_{t }= length after time t. L_{0} = length at the beginning, r = growth rate.

(b) Geometric growth: Geometric growth is the growth where both the progeny cells following mitosis retain the ability to divide and continue to do so. It occurs in many higher plants and in unicellular organisms when grown in nutrient rich medium. Number of cells is initially small so that initial growth is slow which is called lag phase. Later on, there is rapid growth at exponential rate. It is called log or exponential phase.

(c) Sigmoid growth curve: Geometric growth cannot be sustained for long. Some cells die. Limited nutrient availability causes slowing down of growth. It leads to stationary phase. There may be actually a decline. Plotting the growth against time will give a typical sigmoid or S-curve.

S-curve of growth is typical of most living organisms in their natural environment. It also occurs in cells, tissues and organs of plants.

(d) Absolute growth rate is the measurement of total growth per unit time.Relative growth rate is growth per unit time per unit initial growth.

Growth in given time period/ Measurement at start of time period

Suppose two leaves have grown by 5 cm^{2} in one day. Initial size of leaf A was 5 cm^{2} while that of leaf B was 50 cm^{2}. Though their absolute growth is the same (5 cm^{2}/day), relative rate of growth is faster in leaf A(5/5) because of initial small size than in leaf B(5/50).