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Plant Growth and Development - Growth (phases, rates and conditions of growth)

Grade 11CBSEBiology

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Growth in plants is an irreversible permanent increase in size of an organ or its parts or even of an individual cell, usually accompanied by metabolic processes.

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Plant growth is unique because plants retain the capacity for unlimited growth throughout their life due to the presence of meristems at certain locations (Open form of growth).

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Phases of Growth: 1. Meristematic phase (cells divide continuously, have dense cytoplasm and large nuclei). 2. Elongation phase (increased vacuolation, cell enlargement, and new cell wall deposition). 3. Maturation phase (cells attain their maximal size in terms of wall thickening and protoplasmic modifications).

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Growth Rates: The increased growth per unit time is termed as growth rate. It can be arithmetic or geometric.

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Arithmetic Growth: Following mitotic cell division, only one daughter cell continues to divide while the other differentiates and matures. The graph of length against time is linear.

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Geometric Growth: Both daughter cells continue to divide. It consists of a Lag phase (slow), Log/Exponential phase (rapid), and a Stationary phase (growth slows down due to limited resources), forming a sigmoid curve.

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Quantitative comparisons between the growth of living systems can be made in two ways: Absolute Growth Rate (total growth per unit time) and Relative Growth Rate (growth per unit time expressed on a common basis, e.g., per unit initial parameter).

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Conditions for Growth: Water (for cell turgidity and enzymatic activity), Oxygen (for metabolic energy/respiration), Nutrients (for synthesis of protoplasm), and optimum Temperature (usually 28∘C28^{\circ}\text{C} to 30∘C30^{\circ}\text{C}).

📐Formulae

Lt=L0+rtL_t = L_0 + rt (Where Lt=length at time tL_t = \text{length at time } t, L0=length at time 0L_0 = \text{length at time } 0, r=growth rate/elongation per unit timer = \text{growth rate/elongation per unit time})

W1=W0ertW_1 = W_0 e^{rt} (Where W1=final sizeW_1 = \text{final size}, W0=initial sizeW_0 = \text{initial size}, r=relative growth rater = \text{relative growth rate}, t=time of growtht = \text{time of growth}, e=base of natural logarithmse = \text{base of natural logarithms})

Relative Growth Rate=Growth in given time intervalInitial parameter×100\text{Relative Growth Rate} = \frac{\text{Growth in given time interval}}{\text{Initial parameter}} \times 100

💡Examples

Problem 1:

Two leaves, A and B, have areas of 5 cm25 \text{ cm}^2 and 50 cm250 \text{ cm}^2 respectively. After a period of time, both leaves show an increase in area of 5 cm25 \text{ cm}^2. Calculate their Absolute Growth Rate (AGR) and Relative Growth Rate (RGR).

Solution:

For Leaf A: AGR=10−5=5 cm2/timeAGR = 10 - 5 = 5 \text{ cm}^2 / \text{time} RGR=55×100=100%RGR = \frac{5}{5} \times 100 = 100\% For Leaf B: AGR=55−50=5 cm2/timeAGR = 55 - 50 = 5 \text{ cm}^2 / \text{time} RGR=550×100=10%RGR = \frac{5}{50} \times 100 = 10\%

Explanation:

Even though both leaves have the same absolute growth rate (5 cm25 \text{ cm}^2), the relative growth rate of Leaf A is much higher because its initial size was smaller.

Problem 2:

Calculate the final length of a root after 5 hours5 \text{ hours} if its initial length was 2 cm2 \text{ cm} and it shows arithmetic growth at a rate of 0.5 cm/hr0.5 \text{ cm/hr}.

Solution:

Given: L0=2L_0 = 2, r=0.5r = 0.5, t=5t = 5. Using the formula Lt=L0+rtL_t = L_0 + rt: Lt=2+(0.5×5)L_t = 2 + (0.5 \times 5) Lt=2+2.5=4.5 cmL_t = 2 + 2.5 = 4.5 \text{ cm}

Explanation:

In arithmetic growth, the growth is constant over time, so we multiply the rate by the time duration and add it to the initial value.