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 process that attempts to match observation with symbolic statement. A mathematicalmodel uses mathematical language to describe a system. Building a model involves a trade-off between simplicity and accuracy. The success of a model depends on how easily it can be used and how accurate are its predictions.
3
Types of Variables
A mathematicalmodel usually describes a system by a set of variables and a set of equations that establish relationships between the variables. The variables represent some properties of the system. There are four basic groups of variables:
– – – – Input variables Parameters Random variables Decision variables (output variables)
4
The Mathematical Modeling Cycle
Simplify Real World Problem
Interpret
MathematicalModel
Program
Conclusions Simulate
Computer Software
5
The...

...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. computer science,artificial intelligence), but also in the social sciences (such as economics, psychology, sociology and political science); physicists, engineers, statisticians, operations research analystsand economists use mathematicalmodels most extensively.
Mathematicalmodels can take many forms, including but not limited to dynamical systems, statistical models, differential equations, or game theoretic models. These and other types of models can overlap, with a given model involving a variety of abstract structures.
Examples of mathematicalmodels
Population Growth. A simple (though approximate) model of population growth is the Malthusian growthmodel. A slightly more realistic and largely used population growthmodel is the logistic...

...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
This model is useful to find the value of stock, with following assumption should be taken into account while calculating value of stock, which are: 1. That dividends remains to grow continuously on a constant rate 2. The growth rate should remain less than the required return on equity
Relationship between monetary policy and stock market
Monetary policy is a state owned measure which is an an important determinant of stock prices , lowering of increase in interest rate couzld be use by fedration to influence stock prices. it is very useful to find the“value of stock“. Monetary policy effetcs stock prices in two ways:
1.
When in certain circumstances when the federations or the controller of monetray policty lowers interests rates, the return on bonds or securities (which is also considered as an alternative assest to stocks) decreses, this results that the investors who have invested ,are ready or accept to receive a lower required rate of...

...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 that savings has only level effect on income and the growth rate of income depends upon the rate of efficiency or technical progress in the country.
Solow Model relies on certain assumptions
1. There are constant returns to Scale(CRS)
2. The production function is standard neoclassical production function with diminishing returns to factor
3. The markets are perfectly competitive
4. Households save at a constant savings rate ‘s’
Equilibrium in Solow Model is defined as the steady state level of capital where the economy grows at a constant rate. By assuming that the two factors of production are capital and labour per efficiency unit, it can be shown that savings only affects the level of per capita income. It is only the rate of growth of efficiency which determines the rate of growth of per capita output.
For production function: Y= KαL1-α
Steady state values are:...

...Macroeconomics Essay: “Countries grow at 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 model to explain how countries grow, by using the fundamental equation kdot= sf (k) – (n+g+d) k, where k dot is the differential of k with respect to t. The equation shows us how for countries not in the steady state how capital accumulation affects growth and that eventually all countries converge to the steady state. Then once a country has reached its steady state it will be shown that capital accumulation no longer affects economic growth.
Looking at the fundamental equation of the neoclassical growthmodel kdot= sf (k) – (n+g+d) k. It is from this equation that we can see if a country invests more than the break even investment, then kdot increases, i.e. they accumulate capital, and if a country invests less than the break even investment then kdot decreases. The equations shows that all countries will converge to a steady state when investment per effective worker is equal to the...

...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 thismodel, a proxy variable in the form of human capital accumulation is added as an explanatory variable in the cross-country regression. MRW find that human capital accumulation is directly correlated with savings and population growth and the inclusion of human capital lowers the impact of savings and population. MRW claim that by testing the data, they find that this model accounts for 80% of the cross country income variance [cross–section regression of the 1985 level of output per worker
for 98 countries producing an R² of 0.78 ]
The model also predicts that poor countries are likely to have higher returns to human capital. The incorporation of human capital has the ability to tweak the theoretical modeling and the empirical analysis of economic growth. The theoretical impact will be based on the restructuring of growth process ideology. MRW quote Lucas (1988) stating that although there exist decreasing returns to...

...Lalyn C. Nillosa
Blk 166 L16 Calachuchi St. Pembo Makati City
Philippines, 1218
Mobile No.: (63920) 711-8245
Email Add: lalynnillosa@yahoo.com
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.
Weight : 42 kls.
Sex : Female
Civil Status : Single
Religion : Roman Catholic
Nationality : Filipino
EDUCATIONAL BACKGROUND
Elementary Year [From] - [To]
School: Comembo Elementary School 1995 - 2001 Address: Comembo Makati City
Secondary
School: Benigno “Ninoy” S. Aquino High School 2001 - 2005 Address: Comembo Makati City
College 2005 - 2010
Course: Bachelor of Science in Business Administration (College Graduate)
School: University of Makati
Address: J.P. Rizal West Rembo Makati City, Philippines
EMPLOYMENT HISTORY
Position: Administrative Assistant (Regular Crew- Counter Crew, Kitchen Crew)
Company: Jollibee Foods Corporation
Address: SM Makati Ayala Makati City Philippines
Date: Jan. 26, 2009 – March 1, 2013
Reason for Leaving: Resigned
Job Description / Duties and Responsibilities:
• As an Admin Assistant I am responsible in assisting the managers in admin works like monitoring of SPL, office supplies and also in recruiting new employees for the store.
• Responsible in processing of STS (employees...

...
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 countries (Burda and Wyplosz, 2013: 61). This essay aims at examining the aspects of the Solow-Growthmodel of economic growth while highlighting the strengths and weaknesses and identifying whether or not capital accumulation has been the main cause for economic growth in South Africa. This will be achieved through examining economic growth with capital-stock growth, population growth and technological progress.
The Solow-growthmodel measures growth rates of different economies and according to Solow, it is the starting point to determining why these growth rates differ across economies (Burda and Wyplosz, 2013). The Solow-growthmodel is an exogenous growthmodel which means variables are determined outside the field under study, making it a traditional Neo-classical...

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