Biology · Plant Growth and Development · NEET
| Dividing cells | Only ONE daughter cell keeps dividing; other matures | BOTH daughter cells keep dividing |
| Rate of growth | Constant rate | Increases (exponential) rate |
| Graph shape | Straight line (linear) | Upward curve (exponential) |
| Equation | Lt = L0 + rt | W1 = W0 e^rt |
| Example | Root elongating at a constant rate | Log / exponential phase of growth |
In arithmetic growth only one daughter cell divides again after each mitosis; the other one matures and stops. So the number of dividing cells stays the same, and length increases by a fixed amount each day. Plotting length against time gives a straight line. In geometric growth both daughter cells keep dividing, so the number of dividing cells doubles again and again. The increase per day keeps getting bigger, so the graph curves upward (exponential).
For arithmetic growth: Lt = length at time t, L0 = length at the start (time zero), r = growth rate (elongation per unit time), t = time. For geometric growth: W1 = final size, W0 = initial size, r = relative growth rate, t = time, and e = base of natural logarithms (about 2.718). Learn both, because NEET can give you numbers and ask you to calculate.
Yes. Geometric growth is described by the exponential equation W1 = W0 e^rt, so its rapid rising phase is called the exponential phase or log phase. The word geometric points to the pattern (each step multiplies), and exponential points to the equation. In NCERT they mean the same rising curve.
A root elongating at a constant rate is the classic NCERT example of arithmetic growth. Constant rate means the same increase in length every unit of time, which is a straight line. This is a common one-liner NEET fact, so remember: constant-rate root elongation = arithmetic growth.
Yes. A single organ like a root tip can show arithmetic growth (constant elongation), while a whole organism or population of cells often shows geometric growth early on. In most living systems the initial growth is slow (lag phase), then geometric/exponential (log phase), then slows as nutrients run out (stationary phase), which is why the full growth curve is sigmoid (S-shaped).
Try the real previous-year questions from this chapter — each with the answer and a full solution.
In arithmetic growth only one daughter cell keeps dividing after mitosis, so growth is at a constant rate and the graph is a straight line. In geometric growth both daughter cells keep dividing, so growth increases exponentially and the graph is a curve.
Lt = L0 + rt, where Lt is length at time t, L0 is length at the start, r is the growth rate, and t is time.
W1 = W0 e^rt, where W1 is final size, W0 is initial size, r is the relative growth rate, t is time, and e is the base of natural logarithms (about 2.718).
A root elongating at a constant rate is an example of arithmetic growth. The rapid rising (log/exponential) phase of a growing organism or cell population is an example of geometric growth.
Because it follows the exponential equation W1 = W0 e^rt, in which size multiplies over time. Its fast-rising middle part is called the exponential or log phase.
