Learn how to solve for the model’s parameters in a very simple way. This involves such simple skills as reading graphs and tables Ģ) Learn to plot data, using programs such as Excel ģ) Develop a simple exponential model of population growth by understanding its assumptions and learning how to solve a simple first order differential equation. ġ) Learn to use the wealth of available internet resources, such as Google Data, to obtain information on world population. This project follows the lines developed by Banks. Here, I present such a project that I think might achieve multiple specific learning objectives in a very step-by-step fashion, and provide students with a genuine feel for how theoretical mathematics has very real-world applications. This model development makes for an excellent calculus project. Being able to forecast population in the future, and even being able to answer some interesting questions about population in the past, depends on developing accurate mathematical models of population growth. This year, the world’s population passed the 7 billion mark. Therefore, the student is introduced to hyperbolic modeling, and it is demonstrated that with only two population data points, an amazing amount of information can be obtained, such as reasonably accurate doubling times that are a function of t, as well as accurate estimates of such entertaining topics as the total number of people that have ever lived on earth. Moreover, they provide a constant doubling time. This paper, designed to serve as a teaching aid, extends the standard modeling by showing that simple exponential models, relying on two points to fit parameters do not do a good job in modeling population data of the distant past. Keywords: Exponential Growth Modeling Hyperbolic Growth ModelingĪ standard part of the calculus curriculum is learning exponential growth models. Stanford Educational Program for Gifted Youth, Palo Alto, USAĮmail: Decemrevised Januaccepted January 15, 2013
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