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# ALGEBRA WITH APPLICATIONS MATH 141

Virginia Commonwealth University

GPA 3.98

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This 14 page Class Notes was uploaded by Paul Spencer on Wednesday October 28, 2015. The Class Notes belongs to MATH 141 at Virginia Commonwealth University taught by Isabella Ginn in Fall. Since its upload, it has received 28 views. For similar materials see /class/230622/math-141-virginia-commonwealth-university in Applied Math at Virginia Commonwealth University.

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Date Created: 10/28/15

10102011 MATH 141 Math 141 Fall 2011 VCU Sandrine Ngo Table of Contents OVERVIEW STUDY DETAILS SECTION 1 DATA ANALYSIS 11 Data Table 12 Calculate Rate of Change Using erel SECTION 2 VARIABLES OF DATA SET 21 Indicate a riahlpc 22 Domain and Ranga SECTION 3 LINEAR EQUATIONS 31 First Fnlllal39inn 32 Second Equation 33 Fnlllal39inn SECTION 4 IDENTIFY THE SLOPES SECTION 5 IDENTIFY YINTERCEPTS SECTION 6 METHODS FOR CHECKING THE ACCURACY OF MODELS 61 Substitution Methnrl 62 Graphic Methan SECTION 7 PREDICTIONS 71 Estimate Value of Model After 10 years 72 Estimate Value of Model After 50 years SECTION 8 FACTORS CONTRIBUTE DIABETES IN AMERICA SECTION 9 HYPOTHECAL SCENARIO SECTION 10 SUMMARY SECTION 11 REFERENCES Incidence of Diabetes in America Model the increase in number of new cases of diabetes in America since 1995 Sandrine Ngo Math 141 Instructor Ms sabea Brooke Ginn Overview In my project I will study a model of the increase in number of new cases ofdiabetes in America from 1995 to 2009 Based on the reliable data of Centers for Disease Control and Prevention CDC I will analyze the data to find the domain and range and the rate of change of the data set over each year Next I will find equations and compare each equation in order to select one equation which fits with the data set To assure that the model which I am going to choose has an accuracy perfectly I will make an prediction for selected model in 10 years and 50 years past the end year of the data set I will also have a short research about the factors which has caused diabetes in the USA The information for researching is taken from two websites belong to American Government First one is American Diabetes Association and the second is Centers for Disease Control and Prevention CDC For the hypothetical scenario I will come up with assumptions which can affect the rate of change Because of the changing of the rate of change so a new model will be replaced for the old one to make the data set more sense After that a new prediction will be made for checking the validity of the new model Data Analysis 11 Data table 1995 0 80 1996 1 88 1997 2 94 1998 3 105 1999 4 111 2000 5 120 2001 6 129 2002 7 136 2003 8 143 2004 9 152 2005 10 163 2006 11 170 2007 12 178 2008 13 190 2009 14 197 Numberln millions Diabetes in America y 0837x 7844 R2 0998 O Seriesl Linear Seriesl Year 12 The Rate of Change of Data Set The rate of change can calculate by using Excel with the formula Change of fx fb fa Rate Of Change 2 Change of X values b a Slope of line between a faand b fb Year Year started 0 Number In Millions The Rate of Change 1995 0 80 1996 1 88 08 1997 2 94 06 1998 3 105 11 1999 4 111 06 2000 5 120 09 2001 6 129 09 2002 7 136 07 2003 8 143 07 2004 9 152 09 2005 10 163 11 2006 11 170 07 2007 12 178 08 2008 13 190 12 2009 14 197 07 Average of change 0835714286 Variables of Data Set 21 Indicate Variables This data set has two variables which are quotYearquot and quotNumber of People who got diabetic disease in Millionsquot The year will represent for independent variable and the number of people will represent for dependent variable 22 Domain and Range The Domain covers all values in yearcolumn and the Range covers all values in numbercolumn Domain 1995 2009 Or 0 14 Range 80 197 I Linear Equations 31 First equation Y1 The first equation it is taken after plotted a graph from the Excel which is Y1 0837x 7844 32 Second equation Y2 For the second equation the slope m is taken from the average of change in the Excel with the yintercept is the first value in numbercolumn yaxis Y2 0835x 80 33 Third equation Y3 The third equation was found by taking two points from the data set which are 8 143 and 14 197 and then find a slope SI Change offx 197 143 0 9 0pe Change ofx values 14 8 39 m09x8y143 Equation of line Y mx b Plug all the numbers into equation 143 098 b gt b 71 Thus we have an equation Y3 09x 71 IV Identify the Slope in Three Equations Y1 0837x 7844 The slope is 0837 Y2 0835x 80 The slope is 0835 V 09x 71 The slope is 09 The slope of this data set represents the rate of change over time or that means Y increases a certain number for every 1 unit X increases The model for this data falls into a linear pattern so it has a constant rate of change Because of these three slopes are closed to each other thus they have approximate value but we still can check the accuracy of each one by plugging the x value to equations to see which result comes closer to the y value When x 10 Y1 0837x 7844 083710 7844 16214 Y2 0835x 80 083510 80 1635 V 09x 71 0910 71 161 The y value when x 10 or the number of people who were diagnosed diabetic disease is 163millions so the bestfit value is belonged to second equation V Identify the Yintercept in Three Equations Y1 0837x 7844 Yintercept is 7844 V 0835x 80 Yintercept is 80 Y 09x 71 Yintercept is 71 The yintercept in this context means that even if the index were zero that is the year of the initial survey there would still be 80 million cases with diagnosed diabetic disease Compare the yintercepts of three equations the yintercept of the second one showed exactly the same value with the value of yaxis when x 0 After analysis the second equation which is Y2 0835x 80 is better than the others because when we plug any x value into this equation its output is always approximate with the y value respect to x VI Methods of Checking the Accuracy of Models 61 Substitution method For this method we pick randomly any pair of values and substitute them for x and y variables in the equations If the result of any equation is equal or closer to the yvalue that equation must be accurate for the data set Whenx3y 105 Y1 0837x 7844 105 0837x 7844 08373 7844 10355 Y2 0835x 80 105 0835x 80 08353 80 10505 Y3 09x 71 105 09x 71 093 71 98 62 Graphic method Using this method we will plot a graph using two points which were used to illustrate the accuracy of the slopes and yintercepts in section IV and V 1st equation 310355 1016214 2quotd equation 310505 101635 339 equation 39810161 Y1 0837x 7844 Y2 0835x 80 A Y3 09x 71 As we can see because of the slope of three equations are approximate to each other thus they nearly overlap In this situation we can say that three equations are good but the green one is a little bit steepness V Prediction 71 Estimate the Value of Model After 10 years Past The End of the Data Set The year finished the survey of people who got diabetic disease is 2009 so 10 years later is 2019 o If year 1995 is x 0 so year 2019 isx 24 Plug the number of x into the equation Y2 0835x 80 083524 80 284N28 million people got diabetes This number makes sense because if the rate of change remains the same from year to year so in 2019 the number ofdiabetic people will reach 28 million Assume that the population also increases and no medicine is used for treating diabetes 72 Estimate the Value of Model After 50 years Past the End of the Data Set The year finished the survey of people who got diabetic disease is 2009 so 50 years later is 2059 o If year 1995 is x 0 so year 2059 is x 64 Plug the number ofx in the equation Y2 0835x 80 083564 80 614 61 million people got diabetes As the estimation of 10 years past the end of the data set the estimation of 50 years later is also the same We also assume that the rate of change has not changed every year the population also increases and no medicine is used for treating diabetes so in 2059 the number ofdiabetic people will reach 61 million The graph below illustrates for the predictions of 10 and 50 years after 2009 Diabetes in America 0 Seriesl Linear Seriesl Numberln millions VIII Factors Contribute the Increasing of Diabetes in America According to American Diabetes Association there are two types of diabetes which are Type 1 Diabetes and Type 2 Diabetes 0 For Type 1 Diabetes the factors can trigger diabetes are the cold weather and early diet I Cold weather type 1 diabetes spring up more often in winter than in summer and it is much more common in places with cold climates I Early diet this is diagnosed in childhood a gut disorder caused by intolerance to gluten a protein found in wheat o For Type 2 Diabetes this type has a strong relation to family Obesity tends to run in families and families tend to have same eating and exercise habits Based on Centers for Disease Control and Prevention CDC noticed that in the last 2 decades type 2 diabetes has been increasing more often between children and adolescents in the age from 10 to 19 years old in America Every year more than 13 thousands young people diagnosed with type 1 diabetes IX Hypothetical Scenario Assume that population in America has been decreasing since 2009 and assume that American Health Associates gave a fitness program which is called llt is Fun When Exercisequot in this program this Association will distribute an Xbox Kinect Game for every households in America This game requires players have to play actively like playing badminton table tennis soccer or dancing the purpose of this program is help everyone burns their calories to reduce obesity which is one of factors causes diabetes For the two reasons above diabetes in America would decline since 2009 Thus the prediction for 50 years past the end of the data set will be decreased the predictive decreasing number is 40 million people diagnosed with diabetic disease After put this predictive number into the data set and made an observation we can see that the trend line now is going down and it curves So far the previous model which was linear model did not fit with the data any more and a replacement for the linear model is quadratic model Diabetes in America 500 00072 0990x 7350 45390 R2 0997 g 3 y 0514x 1025 g R2 0930 E 300 TE 25390 O Seriesl 20390 Linear Seriesl 5 150 2 100 Poy Seriesl 50 00 Year Quadratic eguation Y 00075x2 09905x 73502 To compare 2 models we predict the value for 60 years past the end of the data set Year 2069 x 74 New linear model Y 0514x 1025 051474 1025 483452 million diabetic people Quadratic eguation Y 00075x2 09905x 73502 00075742 0990574 73502 3957 million diabetic people Now graph the value from quadratic model Diabetes in America 450 400 350 300 250 200 150 100 50 00 O Seriesl Numberln millions Poly Seriesl Year Perfect match X Summary Working as a group is effective but I can see that working alone produces the effect not less than working as a group I worked by myself on this project but I always kept track my works divided the whole process into many subprocesses and completed them on time or early This project has brought to me a profound knowledge about mathematic in particular namely prediction for the trend of a real data knowing clearly the model might change in future if have some factors impact the rate of change of the data In addition I have also known researching for supporting my prediction Xl Reference 1 http rdr quot39 39 39 39 pcv miuulquot39 htm 2 httD diahetes nr diabetesbasicsgeneticsof d39 h hrml 3 http rdr diabetesproiectscda2htm

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