Crude Birth/Death Rates

Tammy Bah
Professor Little
Applied Calculus
Fall '14
Blog #2


Instantaneous Result: Experiment

Part A:
a. My real world application for a question relating to the rate of change is: recorded data from birth and death rates over a period of time in the United State (time vs. birth/death). All of the data in this experiment will be coming from the World Bank Data website.

b. My experiment acts to understand and analyze recorded data from birth and death rates over a period of time.  For this project, I am going to get data on the birth and death rates from 2008 to 2012 of the United States. I thought it was significant to use data from the last 13 years as it is the most relevant and especially for people of my age because we can vividly understand these times. Additionally, there have been many events such as urbanization and the cost of raising and providing for children, especially since the 2008 financial crisis. It is important for us as people to record and research these things because we can see trends when it comes to death and birth rates in America. I would like to add that when I am taking about the birth rate, I am talking the crude birth rate, which means per 1000 people. When I speak of death rates, I am talking about the crude death rate per 1000 people.
Question for this experiment: What is the crude death/birth rate in 2004? Or how can I find the average crude death/birth rate from 2004 to 2012?

c. Create a table of values for the data that you have recorded from your application/experiment.
Table 1:
Years: Birth Rate (per 1,000 people) Death Rate (per 1,000 people)
2004 14.0, 8.3
2005 14.0, 8.3
2006 14.3, 8.1
2007 14.3, 8.0
2008 14.0, 8.2
2009 13.5, 8.4
2010 13.0, 8.0
2011 12.7, 8.1
2012 12.6, 8.1
*All of the data in this experiment will be coming from the World Bank Data website, 6 October 2014

a.     Graph the points using the data from your table of values (connect the dots). 

Graph 1:

b.     Calculate the slope (ARC) of at least three secant lines originating from the same point on your graph to three different points on your graph (i.e. maybe you want to know what happens exactly at x = 20, so your points might be (20, 62), (20, 56), (20, 50)).  Explain what you notice about the ARC of these secant lines and what the calculations mean/represent in terms of your experiment/application.

I will be calculating the slope (ARC) from 2006 to 2011, 2009 to 2011 and 2011 to 2012 for the birth rate (per 1,000 people): *THESE ARE ALL FROM THE BIRTH RATE DATA*

(2006, 14.3), (2009, 13.6), (2011, 12.7) and (2012, 12.6)

ARC from 2006 to 2001—secant line: (13.6-12.7)/(2011-2006)= 0.18

ARC from 2009 to 2011-- secant line  (12.7-13.6)/(2011-2009)= -0.45

ARC from 2011 to 2012--secant line (12.6-12.7)/(2012-2011)= -0.1

From my calculations (slope formula=m=y2-y1/x2-x1), one can see that at the first secant line, the slope is positive at .18; the second and third secant line slopes were negative. I found the ARC for each of the intervals. The tangent line will be at point t=12.7 A negative slope means that in the graph, the line has a negative slope it goes down left to right. As we know, the secant lines get closer and closer to the rate of change. This implies that the birth rate decreases when the year increases and that the birth rate increases when year decreases. However, in terms of data, there is not much of a variety when it comes to the crude death and birth rates, which can affect a graph. Depending on what year it is, the ARC can be wither positive or negative.

c.     Choose a second point (Q) on the tangent line, and calculate the slope of the line (PQ). This calculation will be the instantaneous rate of change ((IRC or derivative at a point)…be sure to identify the units correctly).  Explain what this calculation means mathematically and in terms of your experiment/application.

The second point (Q) on the tangent line will be the IRC between 2011 and 2012:

=(12.6-12.7)/(2012-2011)= -0.1 (decline in crude birth rate from 2011-2012)

This means that in the year of 2011, the IRC for birth rates is -0.1.

The IRC of the situation means that during the years of 2011 to 2012 in terms of the crude birth rate, there was a decline by 0.1, which is correct because if you look at Table 1, the difference between the crude birth rate in 2011 and 2012 is .01(12.7-12.6). decrease in crude birth rate.

We use this IRC to learn and investigate how close the relationship is between the crude death and the birth rate in certain years. This can be to a number of things including having availability to reliable birth control or the infant mortality rate. In the end there was a 0.10 decrease in the crude birth rate. The reason why I did not do this for my project is due to the fact that there is not a good variety for the crude death rates.

*** see tangent line on attached graph (uploaded)

Graph #2: With Tangent

Reference:

"Birth Rate, Crude (per 1,000 People)." The World Bank. Web. 04 Oct. 2014.

"Death Rate, Crude (per 1,000 People)." The World Bank. Web. 04 Oct. 2014