[ Dear student you may consult with other students for help, but under no circumstances take someone work and claim it to be yours]

Size: px

Start display at page:

Download "[ Dear student you may consult with other students for help, but under no circumstances take someone work and claim it to be yours]"

Merryl Young
5 years ago
Views:

1 Project : US National Debt Due: ( 3week period) Prof. Rudy Meangru Your name: ( /42) + 5 extra [ Dear student you may consult with other students for help, but under no circumstances take someone work and claim it to be yours] Our U.S. National debt is a major concern for both lawmakers and citizens. In general, it has been growing at an alarming rate over the past 40 years. The objective of this project is to use data to develop appropriate models both manually and with the use of EXCEL. At the conclusion of this activity students are expected to make some conjecture from their analyses and enhance their knowledge of mathematical modeling. In the exercise below you will incorporate some elementary mathematics concepts that include graphs and exponential function. Task 1: Find a recent article that discusses the U.S. national debt. Write a short paragraph ( 4-5 lines) summarizing the article. (2 pts.). Cite your source. Task 2: Review the table of values below and describe any trend that you observe. (2 pts) Year (t) Debt (billion) , Source: 1

2 Task 3: Search for the amount of the national debt for the years 2016 and (2 points). Cite your source. Task 4: Use Excel to obtain a scatter plot of the above data set in task 2. (5pts) [Label the axes properly] Task 5: Describe the trend of the data from the graph. What type of model do you feel fits this data appropriately? Linear, quadratic or exponential. Explain. (3 points) Task 6: Rescale the values of the year in the above table in task 2. Use t = 0 for the year For example 1970 can be considered as t = 10. This will help you to do any computation with ease. Fill in the missing values in column 1. (2pts) t Debt (billion) Task 7: Assume a linear trend for the last two years in the data set. Find a linear model. ( 5 points) Use (54,17824) and ( 55, 18151) D = at + b a = ( - )/( - ) a = / a = D =?t + b 2

3 Using (54, 17824) to find b =?m + b? =? + b? = b D =?m +? Task 8: Use your model to predict the national debt for the year ( 2 points) D =?m +? D =? ( 60 ) +? (billions) According to this model, the Price is expected to be $ in the year Remark: Finding a quadratic model without a computer program is lengthy and a bit tedious algebraically. Now let s try fitting an exponential model. Task 9: Choose two good points and develop an exponential model for the data.(5 pts) Suppose I choose the points (5,317) and (?,?) We need to find the value of a and b for the function D(t) = ab t D(5) = ab 5 = 317 D(?) = ab? =???? so D D? (?) ab? 5 (5) ab 317 b? =??? b =???????????????? 3

4 ab? =? a(?????? ) 5 = 317 a(??????? ) = 317 a?????? D(t) = ab t A possible exponential function is D(t) = (??????? )(???????) t Task 10 Using your model in task 9 and assume this growth will continue in this fashion, estimate the debt in 2020 (2pts) The value of t is 60 for the year The debt in 2020 can be predicted to be D(60 )= ( )( ) 60 =???? Task 11: Use your EXCEL to obtain a better model. (5pts) Insert the Scatter plot with the exponential curve and equation in it. D( x) =(???? )(e ) (?????x) 4

5 Task 12: Use the better model, to estimate the debt in How does this compare to your earlier model? (2pts) x = 60 (????* 60 ) The debt in 2020 can be predicted to be D( x) =(???? )(e ) =?????? Task 13: Describe the mathematical skills and knowledge you need to complete this assignment. What did you learned from doing this exercise? What was challenging for you in this activity? Based on your analysis of the results of this activity, what do you conclude about the trend of our national debt? (5pts) Task 14 (extra challenge) Graph the scatter plot, the computer generated model and your exponential model on the same pair of axes. Comment on the similarities/differences among the three graphs. ( 5 points) MathEditor 5

EXCEL INSTRUCTION Let s use the table below as a sample to obtain the desired out from EXCEL. Day Expense 1 30.80 2 25.55 3 26.35 4 28.30 5 30.50 6 50.

6 EXCEL INSTRUCTION Let s use the table below as a sample to obtain the desired out from EXCEL. Day Expense Step 1: Access Excel spreadsheet. Step 2: Enter the data set either my typing it in EXCEL or copy from the word file and paste it into EXCEL. 6

Step 3: To obtain a scatterplot, highlight the data set,

Step 4: Make a choice to obatin the scatter plot.

cursor on any dot and right click. A pull-down menu appears.

7 Step 3: To obtain a scatterplot, highlight the data set, select Insert on the menu bar and then Scatter. Step 4: Make a choice to obatin the scatter plot. Step 5: To obtain a regression line or curve, place your cursor on any dot and right click. A pull-down menu appears. Select Add Threadline and choose the required model anlong with Display Equation on chart 7

Linear Regression in two variables (2-3 students per group)

Linear Regression in two variables (2-3 students per group) 1. Choose a 2 or 3 person group. Turn in a list of group members to your instructor, in written form or through email, no later than February,