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MAT200 Inquiry and Problem Solving Competency / Digital Communication Project for eP Depositing
Mathematical Modeling Project (required to be deposited to ePortfolio)
In this project, students will learn how to use their pre-calculus skills to perform quantitative and qualitative
analysis of the raw data in a setting of contextualized learning about relations; namely, they will learn how to employ
Maple computer algebra system to build mathematical models and solve some real life application problems. Students
will represent the data consisting of ordered pairs by the scatter diagram, recognize certain patterns in this scatter
diagram, build an appropriate mathematical model, and, finally, use the model for some predictions and analysis.
Instructions: Copy and paste the heading above into your new opened Maple worksheet. Do not forget to type your
name! Copy and paste the statement of each exercise before you actually do it. Show all the work. Write your
explanations clearly in the Text Mode. The project is to be deposited into Digication. Save/export your Maple
worksheet as PDF with a file name “MAT200 project.” This PDF file will be deposited into ePortfolio under your
instructor’s supervision.
Building Models from the Given Data
A Flavor of Real Life Data and Modeling
Health information databases and, in particular, birth databases are used very often by researchers in health related
disciplines. Let us look at the real data on live birth given by women over 40 years old in Canada since 1974 up to 2005
and analyze this data. Imagine you are a researcher who studies the existing trends in pregnancy outcomes for different
ages of females. Age of 40 and over interests you in particular due to the fact that more and more women tend to plan
having their children late because of their career choices. Plus, the age of 40 and over is also very pro to various health
complications during the pregnancy and birth, as well as negative side effects for newborns (like Down Syndrome, for
The First Task of the Project: In few complete sentences, state the goal of the project, keeping in mind
interdisciplinary audience (use your instructor’s explanations, your own understanding, the first paragraph of this
document and the paragraph above to help organize your thoughts)
Problem (Health and Well-Being, Pregnancy and Birth Outcomes in Canada)
Canadian Vital Statistics provides the following data on pregnancy outcomes (live birth, in particular) for women 40
years and over residing in Canada.1 Suppose you have researched it and found the following data:
Live births (number of events) for females 40 years and over residing in Canada, N
1974 3,737
1975 3,342
1976 3,001
1977 2,462
1978 2,416
1979 2,255
1980 2,123
1981 2,279
1982 2,305
1983 2,262
1984 2,331
1985 2,472
1986 2,682
1987 3,038
1988 3,453
1989 3,699
1990 4,004

Source: Statistics Canada, CANSIM, table 106-9002
MAT200 Inquiry and Problem Solving Competency / Digital Communication Project for eP Depositing
1991 4,262
1992 4,647
1993 5,000
1994 5,415
1995 5,822
1996 6,267
1997 6,598
1998 6,844
1999 7,374
2000 7,924
2001 8,347
2002 8,647
2003 9,214
2004 9,802
2005 10,146
Give complete answers to each of the following questions2
(a) Does the relation defined by the set of ordered pairs (t, N) in the table represent a function? Why or why not? Use
your knowledge of the subject matter to explain and support your conclusion. Answer in full English sentences.
(b) Use the Maple command ScatterPlot to make a scatter diagram. Use t as the independent variable and N as the
dependent variable. Begin your answer to this question with a sentence describing your diagram; for instance, write the
following: “Here is a scatter diagram of the given raw data.” After you plot the diagram, comment (in full English
sentence) on the type of relation that may exist between the two variables based on your observations (linear, quadratic,
polynomial of higher degree, etc.).
(c) Use Maple to find a function of the best fit to the data. Express the relationship using function notation and write
your conclusion.
NOTE: you may choose to work with the original years for time t or you can shift your data and treat 1974 as 0. If you
choose to shift the time line, do not forget to treat every year accordingly. For example, if 1974 corresponds to 0, then
the year of 1975 corresponds to 1, and so on.
(d) Predict the number of live births given by females over 40 in Canada in 2006, 2007, 2010. What makes it possible to
make this prediction? Provide answers in the text mode in full English sentences after you are done working with Maple
(e) Graph the scatter diagram and the graph of the best fit function together. Include an appropriate title.
(f) Reflect on the model: Do you observe a steady increase or decrease in a number of live births given by females over
40 in Canada over the last decades? What do you think might account for this? Research this online and describe your
findings in addition to stating your own opinion (write at least one paragraph; may include images).
(j) More Thinking: What do you think is more reliable: (1) making your predictions far beyond the span (or the range)
of 1974 – 2005; or (2) making predictions within the span (or the range) of a discrete set of given data points or just a
little beyond it? Provide a well-reasoned answer.

2 See Appendix C for help, “Hands-On Laboratory Supplement With Projects. Enhanced Pre-Calculus Learning Experience” in Sullivan and
Sullivan’s Concepts Through Functions, A Unit Circle Approach to Trigonometry (2nd custom edition for LaGCC), Prentice Hall Publishers, 2014.

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