Arithmetic and geometric growth.

• Growth rate is the increase in growth per unit time, so it can be expressed mathematically. The increase may be arithmetic or geometric.
• Arithmetic growth: after mitosis only one daughter cell keeps dividing, while the other differentiates and matures. A root elongating at a constant rate is the simplest example.
• Plotting length against time for arithmetic growth gives a straight line: Lt = L0 + rt, where Lt is length at time t, L0 is length at time zero and r is the growth rate, the elongation per unit time.
• Geometric growth: both daughter cells keep the ability to divide and go on dividing. Growth starts slowly (lag phase), then rises rapidly at an exponential rate (log or exponential phase).
• With limited nutrients, growth then slows and levels off (stationary phase). Growth plotted against time gives a sigmoid or S-shaped curve, typical of living organisms growing in a natural environment and of all cells, tissues and organs of a plant.
• Exponential growth is written W1 = W0 e^rt, where W1 is final size (weight, height, number and so on), W0 is initial size, r is the growth rate, t is time and e is the base of natural logarithms.
• Here r is the relative growth rate, a measure of the plant's ability to produce new plant material, called the efficiency index. The final size W1 therefore depends on the starting size W0.

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