Assignment 4. Indicate with an X the items included in your work.

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Marcia Coral Jefferson
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1 Assignment 4 DESKTOP PUBLISHING (1) Document: Using a word processor, create a useful document (test, handout, overhead transparency, newsletter, etc.) that includes the features listed below. Your file should be a cohesive document and appear as professional and useful as possible. Documents that merely include the listed features, but do not have a clear purpose and cohesive structure are not acceptable. Place a check mark next to each feature you have included. Indicate with an X the items included in your work. X Error checking Two or more pages of text that has been checked for spelling, grammar, style, and readability. X Text Text that includes different fonts, special symbols or equations. X Tables One or more well-formatted data tables. Index/contents Use automatic table of contents or indexing features if appropriate. Styles Use styles to format non-contiguous text within document. Scanned graphics One or more well-formatted, imported, and positioned scanned graphics. Embedded graph, spreadsheet worksheet, organizational chart, word art, or equation. X Embedded graphics X Web graphics Two or more well-formatted and positioned graphics imported from the web. X Edited graphics One or more graphics that you have edited and labeled (this may be one of the graphics above). X Charts & Graphs, Include charts, graphs, or callouts Callouts Movies, Music, speeches Include a movie, speech or musical piece in your file X Text Boxes Use text boxes to position and label graphics. Format your text using linked text boxes so text flows from one box to another. X Formatting Two or more sections of text with distinctly different formats (margins, indents, spacing, number of columns etc.) Annotations Hyperlinks Include three or more of the following: footnotes, endnotes, annotations, appropriate weblinks, headers, footers, or automatic pagination. Download graphics to a local folder. Establish hyperlinks from text in your document to these graphics so you can access them by clicking on the document.

2 An Introduction to Differential Equations And Population growth INDEX General solution of a 1 st order differential equation Derivation and Example Differential modeling of population growth: the equations Graphs, representing population growth The implications of population growth Trouble Spots The General Solution Differential equations come in all sorts of shapes and forms, of which the first order linear is the simplest. A first order linear differential equation has the following form: The general solution is given by where called the integrating factor. If an initial condition is given, use it to find the constant C.

3 Derivation of the General Solution and example of solving a DFEQ Here are some practical steps to follow: 1. If the differential equation is given as rewrite it in the form, where, 2. Find the integrating factor Evaluate the integral Write down the general solution 5. If you are given an IVP, use the initial condition to find the constant C..

4 Models of Population Growth exponential growth: standard logistic growth: logistic growth with a time lag (tau) and/or a non-linear response to population size (theta): Each of these models represents a different set of stipulations and varying parameters in regards to the current and past populations of the world, as well as various other variables. Which of the models below is represented by the graph below?

The Following table reflects some of the parameters that one must consider if they are to properly model a complex and dynamic population such as that of humans.

5 Here is another graph which more clearly demonstrates the exponential growth of the human population. World Population Growth, Source: United Nations, World Population Prospects, The 1998 Revision; and estimates by the Population Reference Bureau. The Following table reflects some of the parameters that one must consider if they are to properly model a complex and dynamic population such as that of humans. After all, the solution to the first order differential equation is merely an approximation, or an idealization, of what really plays out in the real world. World Vital Events Per Time Unit: 2004 (Figures may not add to totals due to rounding) Natural Time unit Births Deaths increase Year 129,358,036 56,150,533 73,207,503 Month 10,779,836 4,679,211 6,100,625 Day 353, , ,021 Hour 14,727 6,392 8,334 Minute Second

6 Effects on the world This type of imbalance cannot continue forever; its easy to extrapolate that as resources become scarcer and the worlds population grows by a billion every decade and a half, we will be subject to all sorts of problems. So what are the effects of this population growth on the rest of the world? The following websites provide us with insight towards these issues: Educators/H uman_population/population_growth/population_growth.htm For a little more practical approach towards the numbers, see this comprehensive website: OR, for a more advanced discussion based more on mathematical theory, check out modeling population growth page: For a descriptive break down of how this reality affects the earth, its resources and its inhabitants, see the following website:

7 Trouble spots Which areas are particularly prone to the effects of population growth? Aka, which areas have the largest current populations?

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