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 >0 ....

...MathematicalModels
Contents
Definition of MathematicalModel Types of Variables The Mathematical Modeling Cycle Classification of Models
2
Definitions of MathematicalModelMathematical modeling is the process of creating a mathematical representation of some phenomenon in order to gain a better understanding of that phenomenon. It is a...

...Mathematicalmodel
A mathematicalmodel is a description of a system using mathematical language. The process of developing a mathematicalmodel is termed mathematical modelling (also writtenmodeling). Mathematicalmodels are used not only in the natural sciences (such as physics, biology, earth science, meteorology) and engineering disciplines (e.g....

...What is Gordon GrowthModel,
“This model is use to determine the fundamental value of stock, it determines the value of stock based on sequence or series of dividends that matured at a constant rate , and the dividend per share is payable in a year”
Stock Value (P) = D / (k – G)--------------Equation 1 Where D= Expected dividend per share one year from now G= Growth rate in dividends k= required rate of return for equity investor...

...Solow model - how well it holds in the real world?
Prepared by:-
Amol Rattan (75013)
Introduction
Prior to Solow Model, Harrod Domar model had shown how the savings rate could play a crucial role in determining the Long run rate of Growth. Solow model however proved a result that was contrary to what Harrod Domar model had predicted.
It showed...

...different rates because they accumulate capital at different rates.” Is this true?
The Neoclassical growthmodel is a framework which we can use to attempt to explain how economic growth behaves. It much simplified model which attempts to explain long run economic growth by looking at capital accumulation, population growth and increases in technical progress. We will use the neoclassical...

...Augmented Solow GrowthModel
The augmented Solow model was proposed by Mankiw, Rower and Weil (MRW) in their treatise “A Contribution to the empirics of Economic Growth”. To better explain the variation in living standards across regions, they propose a model that adds human capital accounting for the fact that labor across different economies can possess different levels of education.
To test this model, a...

...Lalyn C. Nillosa
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PERSONAL INFORMATION
Permanent Address : Blk 166 L16 Calachuchi st. Pembo Makati City, Philippines
Birth Date : June 18, 1988
Birth Place : Paranaque City, Manila
Height : 5’3 ft.
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Sex : Female
Civil Status : Single
Religion : Roman Catholic
Nationality : Filipino
EDUCATIONAL BACKGROUND...

...
The Solow GrowthModel
Economics 202
14 April 2014
Statement on plagiarism: I understand that plagiarism is a serious offence and confirm that unless otherwise acknowledged the content of this essay is my own.
Economic growth rates across countries are hardly ever the same and the Solow-growthmodel is the starting point at determining why growth rates differ across...

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