# Mathematical Model of the Growth of Trees

Good Essays
488 Words
Grammar
Plagiarism
Writing
Score
Mathematical Model of the Growth of Trees
Mathematical Model of the Growth of Trees
Absract
At different stages of life, the growth rate of a tree is not the same. This presentation is to: build a mathematical model according to the regular pattern which has been observed and then solve the problem and optimize the established model.
Problem Proposition A newly planted tree grows slowly, but gradually the tree grows tall and will grow at a faster speed. But when it grows to a certain height, the growth rate will gradually become stable and then slowly go down. This patter is universal.
Problem Analysis If we assume that the growth rate of a tree is proportional with its current height, it obviously does not meet the two ends, particularly the latter part of the growth process, because the tree won't grow faster and faster boundlessly But if we assume that the growth rate of the tree is proportional to the difference between the maximum height and the current height, it is obviously not in conformity with the middle section of the growth process. We made a compromise assuming that the growth rate is proportional with both its current height and difference between the maximum height and the current height.
Assumptions
Assume that there is a maximum height of a tree can grow to, when this height is reached the tree will stop growing higher. Assume that the growth rate of a tree is only related to its current height and the difference between the maximum height and its current height, its not influenced by other environmental factors.
Symbol Descriptors Assume the maximum height of the tree is H (m) and at time t (year) the height is h(m). The proportional coefficient of tree growth rate and the current height and the difference between the maximum height and its current height is k.
Model building and solving According to the analysis of the problem and the assumptions made above, we obtain the following equation: Where the proportional constant k

## You May Also Find These Documents Helpful

• Satisfactory Essays

● Amount of rainfall that runs down the tree. If it is too much, it…

• 406 Words
• 2 Pages
Satisfactory Essays
• Better Essays

| “This was the tree, and it seemed to me standing there to resemble those men, the giants of your childhood, whom you encounter years later and find that they are not merely smaller in relation to your growth, but that they are…shrunken by age.” Ch. 1, Pg. 14…

• 6349 Words
• 26 Pages
Better Essays
• Good Essays

Numerous environmental variables influence plant growth. Three students each planted a seedling of the same genetic variety in the same type of container with equal amounts of soil from the same source. Their goal was to maximize their seedling's growth by manipulating environmental conditions. Their data are shown below.…

• 519 Words
• 3 Pages
Good Essays
• Good Essays

When a plant is placed on a window sill, it grows faster than when it is placed on a coffee table in the middle of the living room.…

• 433 Words
• 2 Pages
Good Essays
• Good Essays

Action affecting Trees = The constant destruction of trees is the one and only factor.…

• 918 Words
• 4 Pages
Good Essays
• Satisfactory Essays

growth’ or branching of the profession began to happen. For example, when a tree grows it starts…

• 254 Words
• 1 Page
Satisfactory Essays
• Satisfactory Essays

1. When a plant is placed on a window sill, it grows faster than when it is placed…

• 283 Words
• 2 Pages
Satisfactory Essays
• Good Essays

Growth is not restricted by shortages of water supply due to the increase in rainfall in the Amazon rainforest. Stratification creates…

• 1275 Words
• 4 Pages
Good Essays
• Good Essays

2. In assessing Raphael’s growth and development, the nurse is guided by principles of growth and development. Which is not included?…

• 4994 Words
• 20 Pages
Good Essays
• Good Essays

The Mt Keira rainforest is located in Wollongong, New South Wales in Australia. The Mt Keira rainforest is what we call a subtropical rainforest. There are four types of rainforest: Tropical, subtropical, warm-temperate and cool-temperate. Tropical rainforests have generally have a warmer climate than subtropical rainforests. Warm-temperate rainforest are slightly cooler than subtropical rainforests, and cool-temperate rainforests have very cool climates, i.e. Canada.…

• 1284 Words
• 6 Pages
Good Essays
• Better Essays

In nature, the oaks hold their own well in competition with the other trees. The oak is a large tree growing to heights of thirty-five to one hundred feet tall. Their leaves are of the most dramatic in shape, which are described as being pinnately veined and pinnately lobed. Meaning the main vein runs through the leaf to its tip and smaller veins branch out, also having deep wavy outline indentations which extend half way or more to the midrib, giving it a hand-like feature. In contrast, the American elm is also a large tree that grows to a height of forty to ninety feet tall and has a simple, short oval shaped leaf that is saw-toothed and lopsided at the base. The trunk of both trees is described as being similar in most ways, thick and covered with furrowed gray bark. The trunks grow lateral with broad branches opening up into a beautiful crown. In time, these dome-headed trees will spread its branches needing a lot of growing space for the canopy. The beauty of the oak tree gives way as it sways in a gentle breeze and flutters its leaves as if waving a happy welcome to anyone who may pass. The elm tree swaying in the same breeze illustrates a simple flat wave.…

• 1112 Words
• 5 Pages
Better Essays
• Good Essays

The author of this article did that, he find out more than basic things and he thinks that it might be a myth. “One study found out that population of Aspen trees had not grown despite a 60% increase in elk.” –Richard Conniff. With this what he meant to say is that this whole time we’ve…

• 382 Words
• 2 Pages
Good Essays
• Good Essays

Aim: To find out how the amount of water available 5m from the ocean and 20m away from the ocean affects the circumference of coconut trees ten metres from the ground.…

• 2812 Words
• 12 Pages
Good Essays
• Powerful Essays

* No population can grow indefinitely due to limited resources such as light, water, and nutrients and also due to competitors and/or predators.…

• 1366 Words
• 6 Pages
Powerful Essays
• Satisfactory Essays

| Counted by looking at a cross section of the tree, looking at how many rings, the ring on the inner most centre is the first growth, and the outside ring is the last.…

• 294 Words
• 2 Pages
Satisfactory Essays