The graph to draw. One graph carrying two plotted lines against the same axes.
x-axis: Age of the teak tree (years), scaled \(\displaystyle 0 \) to \(\displaystyle 40 \) in steps of \(\displaystyle 5 \).
y-axis: Diameter (cm) and Number of annual rings, scaled \(\displaystyle 0 \) to \(\displaystyle 40 \) in steps of \(\displaystyle 5 \) — both quantities happen to share the same range, so one scale serves both.
Line $\displaystyle 1$ — DBH (cm): plot \(\displaystyle (5,4),\ (10,8),\ (20,24),\ (25,28),\ (30,32),\ (40,40) \) and join the points.
Line $\displaystyle 2$ — Number of annual rings: plot \(\displaystyle (5,5),\ (10,10),\ (20,20),\ (25,25),\ (30,30),\ (40,40) \) and join the points. This comes out as a perfectly straight line through the origin at \(\displaystyle 45^\circ \).
Mark each plotted point clearly, use a different symbol or line style for the two lines, and add a key naming them.
(i) Interpretation of the diameter curve
The diameter increases steadily throughout — the teak tree never stops thickening, because its lateral meristem keeps dividing year after year.
Average rate over the whole record: \(\displaystyle \dfrac{40 - 4}{40 - 5} = \dfrac{36}{35} \approx 1.03 \) cm per year.
The rate is not uniform, interval by interval:
\(\displaystyle 5 \to 10 \) yr: \(\displaystyle \dfrac{8-4}{5} = 0.8 \) cm/yr
\(\displaystyle 10 \to 20 \) yr: \(\displaystyle \dfrac{24-8}{10} = 1.6 \) cm/yr
\(\displaystyle 20 \to 25 \) yr: \(\displaystyle \dfrac{28-24}{5} = 0.8 \) cm/yr
\(\displaystyle 25 \to 30 \) yr: \(\displaystyle \dfrac{32-28}{5} = 0.8 \) cm/yr
\(\displaystyle 30 \to 40 \) yr: \(\displaystyle \dfrac{40-32}{10} = 0.8 \) cm/yr
So the curve is steepest between years \(\displaystyle 10 \) and \(\displaystyle 20 \), where girth grows at twice the rate of every other stretch, and settles back to a steady \(\displaystyle 0.8 \) cm/yr after that.
This matches the chapter's account of annual rings: some are wide and some narrow, reflecting favourable or unfavourable growth conditions in that year. The years \(\displaystyle 10\!-\!20 \) were the favourable ones for this tree.
(ii) Relation between diameter and annual rings
The number of annual rings equals the age in years exactly — \(\displaystyle 5, 10, 20, 25, 30, 40 \) rings at \(\displaystyle 5, 10, 20, 25, 30, 40 \) years — so one ring is laid down each year, and counting rings gives the tree's age.
Diameter and ring count rise together: the more rings, the greater the diameter. Each ring is one year's fresh layer of cells added to the girth.
The relation is close to proportional but not exactly so, because rings differ in width: \(\displaystyle \dfrac{4}{5} = 0.8 \) cm per ring at age \(\displaystyle 5 \), \(\displaystyle \dfrac{24}{20} = 1.2 \) cm per ring at age \(\displaystyle 20 \), and \(\displaystyle \dfrac{40}{40} = 1.0 \) cm per ring at age \(\displaystyle 40 \).
Practical use: from a cut trunk, ring count gives the age and ring widths give the climate record of the years the tree grew through.
(iii) The tissue responsible for girth
The lateral meristem.
It is a meristematic tissue of actively dividing cells arranged in a ring along the circumference of the stem — visible in the T.S. of the sunflower stem in Fig. $\displaystyle 3.7$, lying between the phloem outside and the xylem inside.
It divides and produces new cells both inside and outside in concentric layers, and that is what increases the diameter of the stem.
