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INSITTUTO DE ESTUDIOS SUPERIORES DE TAMAPULIPAS

RED DE UNIVERSIDADES AN\303\201HUAC

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M\303\211XICO MMVI

The Population of Mexican United States. Part I

Maple 10 Document

Prepared by

Prof. David Macias Ferrer

E-mail: david.macias@iest.edu.mx

Madero City, Mexico

URL: http://www.geocities.com/dmacias_iest/MyPage.html

<Text-field style="Heading 1" layout="Heading 1">Goals</Text-field>

Given the growth of population from Mexican United States (M\303\251xico) since 1921 to 1995:

To find the curve of better fits for this data through Statistics Package

To find mathematical models for the population behavior using Ordinary Differential Equations and DEtools Pakage

To predict the population in the years 2000 and 2005

<Text-field style="Heading 1" layout="Heading 1">Methodology</Text-field>

The growth of population can be analized by curve fitting tools or differential equations. In this document we will use both methods.

<Text-field style="Heading 1" layout="Heading 1">Applied Problem</Text-field>

According with the National Institute of Satistics, Geography and Informatic (INEGI) of the Mexican government, the population growth since 1921 to 1995 is given by:

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Population (Millions)

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW5HRiQ2J1ElNDguMkYnLyUlYm9sZEdRJXRydWVGJy8lK2ZvcmVncm91bmRHUSpbMjU1LDAsMF1GJy8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGNw==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW5HRiQ2J1ElMTk4MEYnLyUlYm9sZEdRJXRydWVGJy8lK2ZvcmVncm91bmRHUSpbMjU1LDAsMF1GJy8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGNw==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW5HRiQ2J1EjNTlGJy8lJWJvbGRHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1ErWzI1NSwwLDUxXUYnLyUsbWF0aHZhcmlhbnRHUSVib2xkRicvJStmb250d2VpZ2h0R0Y3

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW5HRiQ2J1ElNjYuOEYnLyUlYm9sZEdRJXRydWVGJy8lK2ZvcmVncm91bmRHUSpbMjU1LDAsMF1GJy8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGNw==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW5HRiQ2J1ElMTk5MEYnLyUlYm9sZEdRJXRydWVGJy8lK2ZvcmVncm91bmRHUSpbMjU1LDAsMF1GJy8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGNw==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW5HRiQ2J1EjNjlGJy8lJWJvbGRHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1ErWzI1NSwwLDUxXUYnLyUsbWF0aHZhcmlhbnRHUSVib2xkRicvJStmb250d2VpZ2h0R0Y3

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW5HRiQ2J1ElODEuMkYnLyUlYm9sZEdRJXRydWVGJy8lK2ZvcmVncm91bmRHUSpbMjU1LDAsMF1GJy8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGNw==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW5HRiQ2J1ElMTk5NUYnLyUlYm9sZEdRJXRydWVGJy8lK2ZvcmVncm91bmRHUSpbMjU1LDAsMF1GJy8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGNw==

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbW5HRiQ2J1EjNzRGJy8lJWJvbGRHUSV0cnVlRicvJStmb3JlZ3JvdW5kR1ErWzI1NSwwLDUxXUYnLyUsbWF0aHZhcmlhbnRHUSVib2xkRicvJStmb250d2VpZ2h0R0Y3

91.2

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw==

The graphic is:

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

To find the curve of better fits for this data through Maple 10 Packages and to find mathematical models for the population behavior using Ordinary Differential Equations

<Text-field style="Heading 1" layout="Heading 1">Curve Fitting using Statistics Package</Text-field>

Using Fit and ExponentialFit commands of the Statistics Pakage, we will find a mathematical model that approaches the behavior of the population's growth.

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNjBRIjpGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUlZm9ybUdRJmluZml4RicvJSdsc3BhY2VHUS90aGlja21hdGhzcGFjZUYnLyUncnNwYWNlR0ZPLyUobWluc2l6ZUdRIjFGJy8lKG1heHNpemVHUSlpbmZpbml0eUYn

The vectors of the points dispersion are:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

<Text-field style="Heading 2" layout="Heading 2">Polynomials Fit</Text-field>

Polynomials Fit of Fifth Degree:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

Using Fit command with a Polynomial of fifth degree, we have:

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

print();

The Polynomial Model is:

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

print();

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

Predictions:

The real value of population for 2000 is 97.5 and the predicted value of the Polynomial Model for the same year is:

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

print();

The real value of population for 2005 is 103.3 and the predicted value of the Polynomial Model for the same year is:

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

print();

<Text-field style="Heading 2" layout="Heading 2">Exponential Fit</Text-field>

Exponential Fit

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0Yn

Using the ExponentialFit command we have:

print();

The Exponential Model is:

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

print();

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

Predictions:

The real value of population for 2000 is 97.5 and the predicted value of the Exponential Model for the same year is:

print();

The real value of population for 2005 is 103.3 and the predicted value of the Exponential Model for the same year is:

print();

<Text-field style="Heading 1" layout="Heading 1">Mathematical Models with Ordinary Differential Equation</Text-field>

<Text-field style="Heading 2" layout="Heading 2">Malthusian Model or Exponential Model</Text-field>

In 1798 the Englishman Thomas Robert Malthus (1766-1834) posited a mathematical model of population growth. He model, though simple, has become a basis for most future modeling of biological populations. His essay, "An Essay on the Principle of Population," contains an excellent discussion of the caveats of mathematical modeling.

When the environment is unlimited, the population growth will follow a geometric progression, doubling its size each generation. This growth can be described by a differential equation as:

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

where 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 is the rate of change of numbers over time, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiMtRiw2JVEiYUYnRi9GMkYr is the natural rate of increase and p(t) is the population at any instant. In this model, the parameter LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiMtRiw2JVEiYUYnRi9GMkYr include the constant birth and death rates. We will use the Maple commands to find the Malthusian Model for Mexican population growth.

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

print();

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

print();

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

print();

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

print();

The Malthusian Model is:

print();

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiUtRiw2JVEpTWFsTW9kZWxGJ0YvRjItRiM2OC1JI21vR0YkNjBRIzo9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZELyUpc3RyZXRjaHlHRkQvJSpzeW1tZXRyaWNHRkQvJShsYXJnZW9wR0ZELyUubW92YWJsZWxpbWl0c0dGRC8lJ2FjY2VudEdGRC8lJWZvcm1HUSZpbmZpeEYnLyUnbHNwYWNlR1EvdGhpY2ttYXRoc3BhY2VGJy8lJ3JzcGFjZUdGVi8lKG1pbnNpemVHUSIxRicvJShtYXhzaXplR1EpaW5maW5pdHlGJy1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR1EmMC41ZW1GJy8lJmRlcHRoR0Zeby8lKmxpbmVicmVha0dRJWF1dG9GJy1GLDYlUSdkc29sdmVGJ0YvRjItRj02MFEiKEYnRkAvRkNGMUZFL0ZIRjFGSUZLRk1GTy9GUlEncHJlZml4RicvRlVRLnRoaW5tYXRoc3BhY2VGJy9GWEZicEZZRmZuLUY9NjBRInxmckYnRkBGXXBGRUZecEZJRktGTUZPRl9wRmFwRmNwRllGZm4tRiw2JVEiREYnL0YwRkRGQEZqby1GLDYlUSJwRidGL0YyLUY9NjBRIilGJ0ZARl1wRkVGXnBGSUZLRk1GTy9GUlEocG9zdGZpeEYnRmFwL0ZYUTJ2ZXJ5dGhpbm1hdGhzcGFjZUYnRllGZm5Gam8tRiw2JVEidEYnRi9GMkZecUZpbi1GPTYwUSI9RidGQEZCRkVGR0ZJRktGTUZPRlFGVEZXRllGZm4tSShtYWN0aW9uR0YkNiQtSSptdmVyYmF0aW1HRiQ2I0YuLyUrYWN0aW9udHlwZUdROm1hcGxlc29mdC5jb206bGFiZWwoTDI5MilGJ0YrLUYjNictRj02MFEnJnNkb3Q7RidGQEZCL0ZGRjFGR0ZJRktGTUZPRlEvRlVRJDBlbUYnL0ZYUTN2ZXJ5dGhpY2ttYXRoc3BhY2VGJ0ZZRmZuRltxLUY9NjBRMCZBcHBseUZ1bmN0aW9uO0YnRkBGQkZFRkdGSUZLRk1GT0ZRRmpyL0ZYRltzRllGZm4tSShtZmVuY2VkR0YkNiQtRiM2I0ZlcUZARistRiw2JkYuRi8vJStleGVjdXRhYmxlR0ZERjJGaW4tRj02MFEiLEYnRkBGQkZpckZHRklGS0ZNRk9GUUZqckZcc0ZZRmZuLUYjNjZGW3FGXnMtRmNzNiQtRiM2Iy1JI21uR0YkNiRRIjBGJ0ZARkBGaHEtRmV0NiRRJTE0LjNGJ0ZARmluLUY9NjBRInxockYnRkBGXXBGRUZecEZJRktGTUZPRmFxRmFwRmNxRllGZm5GW3RGaW4tRiw2JVEldHlwZUYnRi9GMkZocS1GLDYlUShudW1lcmljRidGL0YyRlt0RmluLUYsNiVRJnJhbmdlRidGL0YyRmhxRmR0LUY9NjBRIy4uRidGQEZCRkVGR0ZJRktGTUZPRmFxL0ZVUTBtZWRpdW1tYXRoc3BhY2VGJ0Zhc0ZZRmZuLUZldDYkUSM3NkYnRkBGXnEtRj02MFEiOkYnRkBGQkZFRkdGSUZLRk1GT0ZRRlRGV0ZZRmZuRitGKw==

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

Predictions:

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

print();

The real value of population for 2000 is 97.5 and the predicted value of the Malthusian Model for the same year is:

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

print();

The real value of population for 2005 is 103.3 and the predicted value of the Malthusian Model for the same year is:

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

print();

<Text-field style="Heading 2" layout="Heading 2">Verhulst-Pearl Model or Logistic Model</Text-field>

As the exponential growth cannot be maintained indefinitely because ressources become limiting we need to add a second element limiting the rate of growth. The differential equation could be modified to take in account the dampening effect of intraspecific competition as

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

where 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 is the population size at any instant, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== is the intrinsic rate of increase and, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJw== is the carrying capacity, that measures the population size that can be supported by the environment at balance.This equation has been developped independently by the mathematician and biologist Belgian Pierre Francois Verhulst (1804-1849) in his essay "Notice sur la loi que la Population suit dans son Accroissement" (1938) and the geneticist and enviromentalist Raymond Pearl (1879-1940) in his work "The Biology of Population Growth" (1925). In this case, we will take LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNjBRIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUlZm9ybUdRJmluZml4RicvJSdsc3BhY2VHUS90aGlja21hdGhzcGFjZUYnLyUncnNwYWNlR0ZPLyUobWluc2l6ZUdRIjFGJy8lKG1heHNpemVHUSlpbmZpbml0eUYnLUkjbW5HRiQ2JFEpMC4wMzA0MzFGJ0Y5 and LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiYkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNjBRIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUlZm9ybUdRJmluZml4RicvJSdsc3BhY2VHUS90aGlja21hdGhzcGFjZUYnLyUncnNwYWNlR0ZPLyUobWluc2l6ZUdRIjFGJy8lKG1heHNpemVHUSlpbmZpbml0eUYnLUkjbW5HRiQ2JFEnMjk4LjM0RidGOQ==

QyQ2JS1JJXdpdGhHNiI2I0koREV0b29sc0dGJi1GJTYjSSZwbG90c0dGJi1GJTYjSStTdGF0aXN0aWNzR0YmISIi

Pkkkb2RlRzYiLy1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJwR0YkNiNJInRHRiRGLSomRioiIiIsJiQiJkovJCEiJ0YvKiYkIiQtIkYzRi9GKkYvISIiRi8=

print();

LUknZHNvbHZlRzYiNiNJJG9kZUdGJA==

print();

PkkmY2luaTJHNiIvLUkicEdGJDYjIiIhJCIkViIhIiI=

print();

LUknZHNvbHZlRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiM8JEkmY2luaTJHRidJJG9kZUdGJw==

print();

LUkmZXZhbGZHJSpwcm90ZWN0ZWRHNiNJIiVHNiI=

print();

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEhRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiVGKy1GIzYoLUYsNiVRJXBvYjFGJ0YvRjItSSNtb0dGJDYwUSM6PUYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRC8lKXN0cmV0Y2h5R0ZELyUqc3ltbWV0cmljR0ZELyUobGFyZ2VvcEdGRC8lLm1vdmFibGVsaW1pdHNHRkQvJSdhY2NlbnRHRkQvJSVmb3JtR1EmaW5maXhGJy8lJ2xzcGFjZUdRL3RoaWNrbWF0aHNwYWNlRicvJSdyc3BhY2VHRlYvJShtaW5zaXplR1EiMUYnLyUobWF4c2l6ZUdRKWluZmluaXR5RictRiw2JVElcGxvdEYnRi9GMi1GPTYwUTAmQXBwbHlGdW5jdGlvbjtGJ0ZARkJGRUZHRklGS0ZNRk9GUS9GVVEkMGVtRicvRlhGYG9GWUZmbi1JKG1mZW5jZWRHRiQ2JC1GIzZBRistRj02MFEiW0YnRkAvRkNGMUZFL0ZIRjFGSUZLRk1GTy9GUlEncHJlZml4RicvRlVRLnRoaW5tYXRoc3BhY2VGJy9GWEZfcEZZRmZuRistRmNvNiYtRiM2JS1JI21uR0YkNiRRIjBGJ0ZALUY9NjBRIixGJ0ZARkIvRkZGMUZHRklGS0ZNRk9GUUZfby9GWFEzdmVyeXRoaWNrbWF0aHNwYWNlRidGWUZmbi1GZnA2JFElMTQuM0YnRkBGQC8lJW9wZW5HRmlvLyUmY2xvc2VHUSJdRidGaXAtRmNvNiYtRiM2JS1GZnA2JFEiOUYnRkBGaXAtRmZwNiRRJTE2LjZGJ0ZARkBGYnFGZHFGaXAtRmNvNiYtRiM2JS1GZnA2JFEjMTlGJ0ZARmlwLUZmcDYkUSUxOS43RidGQEZARmJxRmRxRmlwLUZjbzYmLUYjNiUtRmZwNiRRIzI5RidGQEZpcC1GZnA2JFElMjUuOEYnRkBGQEZicUZkcUZpcC1GY282Ji1GIzYlLUZmcDYkUSMzOUYnRkBGaXAtRmZwNiRRJTM0LjlGJ0ZARkBGYnFGZHFGaXAtRmNvNiYtRiM2Li1GZnA2JFEjNDlGJ0ZARmlwLUZmcDYkUSU0OC4yRidGQC1GLDYmRi5GLy8lK2V4ZWN1dGFibGVHRkRGMi1GPTYwRmZxRkBGam9GRUZbcEZJRktGTUZPL0ZSUShwb3N0Zml4RidGXnAvRlhRMnZlcnl0aGlubWF0aHNwYWNlRidGWUZmbkZpcC1GY282Ji1GIzYlLUZmcDYkUSM1OUYnRkBGaXAtRmZwNiRRJTY2LjhGJ0ZARkBGYnFGZHFGaXAtRmNvNiYtRiM2JS1GZnA2JFEjNjlGJ0ZARmlwLUZmcDYkUSU4MS4yRidGQEZARmJxRmRxRmlwLUZjbzYmLUYjNiUtRmZwNiRRIzc0RidGQEZpcC1GZnA2JFElOTEuMkYnRkBGQEZicUZkcUYrRkBGYnFGZHFGaXAtRj02MFExJkludmlzaWJsZVRpbWVzO0YnRkBGQkZFRkdGSUZLRk1GT0ZRRlRGV0ZZRmZuLUYsNiVRInRGJ0YvRjItRj02MFEiPUYnRkBGQkZFRkdGSUZLRk1GT0ZRRlRGV0ZZRmZuRmVwLUY9NjBRIy4uRidGQEZCRkVGR0ZJRktGTUZPRl91L0ZVUTBtZWRpdW1tYXRoc3BhY2VGJ0Zhb0ZZRmZuLUZmcDYkUSM3NkYnRkBGaXBGYXctRiw2JVEmc3R5bGVGJ0YvRjJGZ3ctRiw2JVEmcG9pbnRGJ0YvRjJGaXBGYXctRiw2JVEqdGhpY2tuZXNzRidGL0YyRmd3LUZmcDYkUSIyRidGQEZARistRj02MFEiOkYnRkBGQkZFRkdGSUZLRk1GT0ZRRlRGV0ZZRmZuRis=

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

Predictions:

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

print();

The real value of population for 2000 is 97.5 and the predicted value of the Verhulst-Pearl Model for the same year is:

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

print();

The real value of population for 2005 is 103.3 and the predicted value of the Verhulst-Pearl Model for the same year is:

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

print();

Legal Notice: The copyright for this application is owned by the author(s). Neither Maplesoft nor the author are responsible for any errors contained within and are not liable for any damages resulting from the use of this material. This application is intended for non-commercial, non-profit use only. Contact the author for permission if you wish to use this application in for-profit activities.

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