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Mathematical Modeling Project (required to be deposited to ePortfolio) MAT200 Name: Hamid Ninach Goal of the project: The goal of this project is to accomplish a quantitative and qualitative analysis of the raw data and build mathematical models and relations. In addition to that, to enable students to get familiar with and use Maple to solve real life problems. Furthermore, the purpose of this project is to analyze this data to see if live births for females 40 years and over residing in Canada have problems during pregnancy and after giving birth, as well as negative side effects for newborns like Down Syndrome. So, the goal of this project is to solve real-life application problems and to do some predictions and analysis of the data collected. 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: Annual, t

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

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

(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.

Answer: Yes the relation defined by the set of ordered pairs (t, N) in the table represent a function because every input (first coordinate) has one output (second coordinate). In other words, one value in the Domain has one corresponding value in the Range. (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 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.). > >

(1)

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Answer: we can observe from the scatter plot that the relation between the two variables appears to be quadratic in nature. (c) Use Maple to find a function of the best fit to the data. Express the relationship using function notation and write your conclusion. I choose to shift the time line. 1974 corresponds to 0, then the year of 1975 corresponds to 1, and so on to 2005 corresponds to 31. >

(3) > (4) > (5) > (6) f(x) = 2996.-155.2 x+12.98 x^2 is the quadratic function of best fit that models the relation above.

(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 commands. 2006 corresponds to 32, 2007 corresponds to 33 and 2010 corresponds to 36. > 11321.12 > 12009.62 > 14230.88 > The numbers above show that live births given by females over 40 are increased due to the evolution of medicine and health.

(e) Graph the scatter diagram and the graph of the best fit function together. Include an appropriate title. >

(7) (8) (9)

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(f) by females of 40 years old and over in Canada and find this minimum number of births. In other words, use your model and your knowledge of Pre-Calculus material to approximate the minimum number of births in the span of years provided. Explain your steps to get a full credit.

Answer: The year

corresponds to the value X that that minimize the number of live births were given by females of 40 years old and over. In other words, it corresponds to the first coordinate of the vertex of the parabola, and we can find it using the coefficients a,b and c by computing The minimum number corresponds to the second coordinate of the vertex. Thus, answering this question boils down to figuring out what the vertex of the parabola is. >

(10) > (11) > 5.978

(12)

> (13) > 2532.073960

(14)

2532.

(15)

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Conclusion: According to this quadratic model, the year in span of

of live births were given by females of 40 years old and over is approimitaly T=6 and that corresponds to the year 1980. Therefore, this year 1980 gives the minimum number of live births were given by females of 40 years old and over and this minimum number is 2123 live births.

(j) 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 and 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). Answer: According to the model I notice a constant increase in a number of live given by women over 40 in Canada and over in the last decades. The reasons that might account for this are many women in their 20s and 30s are completing educations and starting careers. They feel unready financially and to have babies. Also, some women wait a long time to find the right person to marry him and have children. Moreover, many women have confidence self in their own continued fertility or the ability of doctors to help. In my opinion, technological development, especially in the field of medicine and women's exit to work, are the main reasons that make women wait until age 40 and over to give live births. (k) More Thinking: What do you think is more reliable: (1) making your predictions far beyond the discrete set of given data points or just a little beyond it? Provide a well-reasoned answer.

Answer: I think that making predictions within the range of a discrete set of given data points or just a little beyond it is more reliable. In my opinion, it is more reliable because it works as a guide to predicting a set of data points with a better chance of exactitude. The information obtained is often supported by real-time events or experiments, which

can also be drawn on the graph, providing a visual representation of what we are looking for. This allows us to foretell the increase in live births as the margin of error decreases....