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Q3(b):
Describe briefly: (b) Geometric growth

Solution :

Theoretical Foundation: Geometric Growth

Geometric growth refers to a pattern of development in plants where both daughter cells resulting from mitosis retain the ability to divide and continue the cell cycle. Unlike arithmetic growth, where only one cell lineage remains meristematic, geometric growth leads to an exponential increase in total cell number [Per the principles of cell kinetics in meristematic tissues].

Step 1: The Exponential Model

In geometric growth, the plant follows an exponential distribution of biomass or cell count. If $N_0$ is the initial number of cells at time $t=0$, and $N_t$ is the number of cells at time $t$, the relationship is governed by the following mathematical expression:

$N_t = N_0 e^{rt}$

  • $N_t$: Final size (weight, height, or number).
  • $N_0$: Initial size at the beginning of the period.
  • $r$: Relative growth rate (the efficiency index).
  • $t$: Time of growth.
  • $e$: Base of natural logarithms ($\approx 2.71828$).

Step 2: Visualizing Geometric Progression

The progression of cell division follows a $2^n$ sequence. Initially, growth is slow (lag phase), followed by a rapid, explosive increase (log or exponential phase).

Time (t) Size (N) Exponential Growth Curve

Step 3: Comparative Analysis

Feature Geometric Growth
Cell Division Both daughter cells divide.
Growth Rate Constant relative growth rate.
Resulting Curve Sigmoid or 'S'-shaped curve (in closed systems).
Mathematical Law $W_1 = W_0 e^{rt}$

Step 4: Biological Significance

Geometric growth is predominantly observed in the early developmental stages of embryos and in the proliferation of undifferentiated callus tissue [Per experimental observations in plant tissue culture]. Because all cells produced are mitotically active, the increase in plant volume or biomass is proportional to the amount of biomass already present at any given time $t$.

Final Solution: Geometric growth is a mode of development characterized by exponential proliferation where all resultant daughter cells remain meristematic, represented by the equation $W_1 = W_0 e^{rt}$, typically resulting in a sigmoidal growth curve when nutrient resources are limited.


More Questions from Class 11 Biology Plant Growth and Development EXERCISES


CBSE Solutions for Class 11 Biology Plant Growth and Development


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