Biology · Plant Growth and Development · NEET
The formula is Lt = L0 + rt. Here L0 is the length at time zero (starting length), r is the growth rate (elongation per unit time, for example cm per day), t is the time, and Lt is the length after time t. You simply multiply the rate by the time and add it to the starting length. Example: if L0 = 20 cm, r = 30 cm/day and t = 7 days, then Lt = 20 + 30 x 7 = 20 + 210 = 230 cm.
Use Lt = L0 + rt for arithmetic growth, where growth is at a CONSTANT rate (only one daughter cell keeps dividing, like a root elongating steadily). Use Wt = W0 e^rt for geometric or exponential growth, where BOTH daughter cells keep dividing, so growth speeds up (log phase). If the question says 'constant rate' or gives you a straight-line graph, use the arithmetic formula. If it says 'exponential' or gives r as a relative growth rate, use the exponential formula.
In arithmetic growth (Lt = L0 + rt), r is the growth rate or elongation per unit time, for example 30 cm per day. In geometric growth (Wt = W0 e^rt), r is the relative growth rate, also called the efficiency index, which measures how fast the plant produces new material per unit of existing material. So the SAME letter r means slightly different things in the two formulas.
For arithmetic growth, put t = n (the day number) into Lt = L0 + rt. So length on day n = starting length + (rate x n). For example, to find the length at the end of the 7th day with L0 = 20 cm and r = 30 cm/day: L7 = 20 + (30 x 7) = 230 cm. Do NOT multiply the starting length by the days; only the added growth (rt) uses the number of days.
Absolute growth rate is the total growth per unit time (for example, a leaf grew 5 cm2 in 1 day, so absolute rate = 5 cm2/day). Relative growth rate is growth per unit time expressed per unit of the STARTING size (for example, that same 5 cm2 growth on a small leaf of 5 cm2 gives a relative rate of 5/5 = 1 per day). A small leaf and a big leaf can add the same absolute amount, but the small leaf has a higher relative growth rate.
Yes. When you plot length (Lt) against time (t) for arithmetic growth, you get a straight line. The slope of that straight line is exactly r, the constant growth rate. This is why arithmetic growth gives a linear graph, while geometric growth gives a J-shaped exponential curve.
Length of the stem at time 0 is 20 cm. The arithmetic growth rate is 30 cm per day. What is the length of the stem at the end of the 7th day?
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Lt = L0 + rt, where L0 = starting length, r = constant growth rate per unit time, t = time, and Lt = length after time t. It gives a straight-line (linear) graph.
Wt = W0 e^rt, where W0 = initial size, r = relative growth rate, t = time, e = base of natural log (about 2.718), and Wt = final size. It gives a J-shaped exponential curve.
Because the rate r is constant, the same amount is added in each unit of time. Plotting length against time therefore gives a straight line whose slope equals r.
Exponential (geometric) growth becomes much faster over time because both daughter cells keep dividing, so growth compounds. Arithmetic growth stays steady because only one daughter cell keeps dividing.
In Wt = W0 e^rt, r is the relative growth rate, also called the efficiency index. It measures the plant's ability to produce new material per unit of existing material.
