TAILIEUCHUNG - Application of differential equation to population growth

Thomas Malthus, an 18th century English scholar, observed an essay written in 1798 that the growth of the human population is fundamentally different from the growth of the food supply to feed that population. He wrote that the human population was growing geometrically [. exponentially] while the food supply was growing arithmetically [. linearly]. He concluded that left unchecked, it would only be a matter of time before the world's population would be too large to feed itself. The first growth model we examine in this module is the one Thomas Malthus referred to in his famous essay. Malthus' model is considered a more sophisticated model for the special case of world population. | APPLICATION OF DIFFERENTIAL EQUATION TO POPULATION GROWTH Harideo Chaudhary ABSTRACT Thomas Malthus an 18th century English scholar observed an essay written in 1798 that the growth of the human population is fundamentally different from the growth of the food supply to feed that population. He wrote that the human population was growing geometrically . exponentially while the food supply was growing arithmetically . linearly . He concluded that left unchecked it would only be a matter of time before the world s population would be too large to feed itself. The first growth model we examine in this module is the one Thomas Malthus referred to in his famous essay. Malthus model is considered a more sophisticated model for the special case of world population. Key words population equation differential growth and logistic. INTRODUCTION Malthus model is commonly called the natural growth model or exponential growth model. For this we assume that the population grows at a rate that is proportional to itself Banks 1999 . If P represents such population then the assumption of natural growth can be written symbolically as dP dt k P Where k is a positive constant. This model has many applications besides population growth. For example the balance in a savings account with interest compounded continuously and no withdrawals exhibits natural growth. In this case the constant k is called the annual rate of interest. Also large animal populations whose size is not constrained by environmental factors grow exponentially. In this setting k is called the productivity rate of the population. NAIVE MODEL EXPONENTIAL GROWTH It is possible to explain the various growth phenomena with mathematical model some of them are simple and some are complicated. The most famous example is the familiar Malthusian or exponential growth model in differential equation form it has the equation dP KP dt Where P is the magnitude of growing quantity t is the time and k is the growth .

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• Application of differential equation
• Population growth
• Differential equation
• Growth and logistic
• Special case of world population
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• differential equations class 1
• linear equation 1
• the application of differential equations
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