Long Answer
Medium difficulty • Structured explanation
Question 1
Long FormCompare arithmetic and geometric growth in plants with respect to their pattern, mathematical expressions, and the type of growth curve each produces.
- In arithmetic growth, only one daughter cell continues to divide after mitotic cell division while the other differentiates and matures; a root elongating at a constant rate is the simplest example.
- The mathematical expression for arithmetic growth is Lt = L0 + rt, where Lt is the length at time t, L0 is the initial length, and r is the constant growth rate; plotting length against time yields a linear curve.
- In geometric growth, both progeny cells following mitosis retain the ability to divide and continue to do so; growth is initially slow (lag phase) and then increases rapidly at an exponential rate (log phase) before levelling off in a stationary phase due to limited nutrients.
- The exponential growth formula is W1 = W0 e^rt, where r is the relative growth rate (efficiency index) and W1 depends on the initial size W0; plotting growth parameter against time produces a sigmoid (S-shaped) curve.
- The sigmoid curve is characteristic of living organisms in natural environments and is typical for all cells, tissues, and organs of a plant.
- The key difference is that arithmetic growth leads to a constant, linear increase, while geometric growth leads to exponential increase followed by a plateau, reflecting real biological resource constraints.