LSP 120 Final Review

Linear Modeling

1.  Open the file USTobacco.xls which contains data on the total amount of tobacco produced in the US.

a. Make an XY scatter plot of the data. Include it in your document.  Add a linear trendline to your plot, including the equation and the R-squared value.

b. Use the equation in b. to predict the amount of tobacco produced in 2002.

c. How much confidence do you have in your prediction? Write at least three sentences justifying your prediction including a lead sentence, at least two supporting sentences and any items that that must be pointed out (if applicable).

Exponential Modeling and Solving Exponential Equations

2. Carbon dioxide emissions from the burning of fossil fuels is almost surely a cause of global warming.  One of the difficulties in negotiating a treaty for the reduction of carbon dioxide emissions is the discrepancy in emission levels between developing and developed nations.  For example, in 1999, Brazil emitted 89 million metric tons of carbon into the atmosphere, while Canada, a much less populous country, emitted 151 million metric tons.  Brazil’s emissions, however, are growing at 4.1% per year, while Canada’s are growing at 0.8%.

1. In Excel, make a table and using what you learned about exponential growth (percent increase), calculate when Brazil’s emissions will exceed Canada’s. Paste your table on your word document.

2. How much confidence you have in your prediction in b?

3. Find formula for the exponential function which models Brazil’s emissions (using 1999 as year 0).

4. Using the formula for Brazil’s model, predict Brazil’s emissions in 2010.

3. In 1994, some samples from the archeological site at Oslonki, Poland were dated using carbon 14.  The archeological site is significant for the large quantities of copper implements and jewelry found there.  One of the samples had 47.8% of the carbon 14 that would normally be present in a living organism.  (Carbon 14 decays approximately 1.202% every 100 years.)

a. Using Excel calculate the approximately how old the sample is.  Paste the Excel table you used to calculate your answer.

b. Using logs calculate the exact age of the sample. Show your calculation.

4.  In 1990, the population of the town Erehwon was 5000 and has been increasing by 2.9% every year.  The population of the town Exalpon, Erehwon’s nearest neighbor, was 4500 and increasing by 3.2% every year.  When, will the population of Exalpon exceed Erehwon?

Trendlines and Graphs

5.  Below is a trendline graph of the number cellular telecommunications subscribers from 1994 - 2003.

1. Based on what you learned about creating effective graphs, list two concerns about the above graph.

2. Predict when there were no cell phone subscribers? (Since you do not have the data, use the slope and intercept that is given to you in the formula in the graph to calculate your answer)  How much faith do you have in your prediction?

3. How much faith do you have in your prediction?

4. Using your equation, predict the number of subscribers in 2030. 

6. Open the file EarnedDegreesbyLevelandGender.xls which contains data on degrees conferred in 2006.

1. Make a single graph to answer this question: In 2006 what percentage of all degree-earning males and what percentage of all degree-earning females earned a Doctoral degree?

2. Make a single graph to answer this question: In 2006 what percentage of all those receiving a Doctoral degree were female and what percentage were male?

Percentages and Rates

7.  The following table list the 2009 average circulation of ten magazines with the largest circulation in the US.

1. How many times larger is the circulation of AARP The Magazine greater than the circulation of National Geographic?

2. By how many percent is the circulation of Reader's Digest larger than the circulation of Family Circle?

3. The magazine that had the largest circulation in the United Kingdom was the entertainment magazine Skymag.  Its 2009 circulation was 7,545,510.  By how many percent is its circulation larger than the circulation of the National Geographic?

4. In 2005 the magazine TV Guide was ranked 4th in the nation with a circulation of 8,211,581. Just four years later it had fallen to 22nd place with a circulation of 2,934,969. By how many percent did the circulation drop from 2005 to 2009?

8.  In the period January 2000 to March 2000, stock for Sapient Corporation, a consulting company that helps businesses put their operations on the internet, dropped 51% and then rose by 49%.  By how many percent did price change over the whole period?

9. Cigarette use in the US has decreased over the last 20 years, even though the rate is still relatively high.  In 1998, 277 of every 1000 individuals in the US over the age of 12 reported that they were smoking, a 28% decrease since 1985.  What was the rate in 1985?

10.  At DePaul University, minority students represented 31% of the enrollment in 2001. If there were 21,363 students enrolled in 2001, about how many of these students are minority students?

11.  Chicago’s population grew from 2.78 million in 1990 to 2.90 million in 2000.  By how many percent did it grow?

12.  The January 14, 2002 issue of TIME magazine reported that Wal-Mart’s 3rd quarter revenues for 2001 were 600% more than its No. 2 competitor, K-Mart.  What were K-Mart’s revenues during this period if Wal-Mart’s revenues were $48 billion? 

13.  In 2006, 261.9 million people in the United States were born in the United States, and the rest, 37.5 million were foreign born.  What percentage of the population of the US was foreign born?

14.  Over the last four years, DePaul’s freshman class has grown by 4.8%.  What is the Fall 2005 freshman enrollment if the 2009 enrollment was 3,041 students? 

15.  In 2001, 6,113 applicants were accepted to DePaul. This represents about a 72% acceptance rate. Of the students who were accepted, 2,050 students enrolled at the university.

1. How many students in 2001 applied for admission at DePaul?

2. What percent of the students who were accepted to DePaul actually enrolled at the University?

16.  The November 16, 2009 issue of the New York Times  reported that there were 671,616 foreign students enrolled at US colleges and universities in 2008-09 — representing an 8% increase from the previous year. It was the largest percentage increase in more than 25 years. 

1. How many foreign students were studying in US colleges and universities during 2007-2008?  

2. The greatest number (103,260) of foreign students came from India.  What percent of the foreign students studying in the US were from India?  

3. China currently has the second largest number of foreign students studying in the US, however they are rapidly catching up to India. The number of foreign students from China in 2007-2008 was 81,413. That number grew by 21% over the next year. How many foreign students were from China during 2007-2008?

17.  The December 11, 2002 issue of Sports Illustrated reported that the federal spending for Olympic Games held in the United States was $610 million for the 1996 Atlanta Games and $1.5 billion for the 2002 Salt Lake City Games. (The figures have been adjusted for inflation.)

1. How many times more federal money was spent on the Salt Lake City Games than the Atlanta Games?

2. By what percent  is the federal spending for the Salt Lake City Games more than the Atlanta Games?

3. By what percent is the federal spending for the Atlanta Games less than the Salt Lake City Games?

Consumer Price Index

18. Carefully describe a) what the CPI is, b) how it is constructed, and c) what the meaning of actual index numbers is (e.g., the CPI in 1999 was 166.6; what does 166.6 mean?)

19. Open the Defense.xls file. this file contains the data on U.S. spending for national defense for fiscal years between 1960 and 2002.

1. Using the CPI, add a column to the table in which you calculate defense spending for these years in constant 2002 dollars, and cut and paste the table into your word document. 

2. Create an XY graph showing spending in constant 1999 dollars for the period 1960-2002.

3. In a well written paragraph describe the graph you made in c.

20. According to the Defense.xls file, spending for national defense in 1985 was $279 billion and in 2002 it was $399.5 billion. 

1. Discuss why you cannot conclude that the spending on defense increased in value from 1985 to 2002.

2. Using the information in CPI.xls, convert the 1985 actual spending to 2002 constant dollars.  Compare this value to the actual 2002 spending.  What does it tell you about defense spending over these years.

3. The 2002 constant dollar value of the 1985 spending is what percent larger than the actual spending in 2002?

Loans

21.  You have decided to buy a 2003 Chevy Cavalier. The total cost with tax, title, license and optional equipment is $20,500. You will make a down payment equal to 10% of the total cost of the car. The remaining amount will be financed.

You have two financing options.

Option 1 - Get $2,500 cash back. This amount will reduce the amount you need to finance. You will be able to get a 5 year car loan on the remaining amount with a 6.0% interest rate from your bank.

Option 2 - Get no cash back and finance the entire amount. The loan will be for 3 years with a 0.0% interest rate from GMAC financing.

1. What is the amount of money that you will need to borrow under Option 1? 

2. Make an amortization table for Option 1 and verify that your ending balance after 60 months is zero. Paste the first five lines (months 0 - 4) in your Word document. What is your monthly payment? What is the total amount paid over the term on the loan?

3. How much will you need to borrow if you choose option 2? What is your monthly payment?

4. Which financing option should you choose? Explain. 

Credit Cards

22.  You only use your credit card in the case of an emergency. You charge $4,000 in auto repairs to credit card which has an annual interest rate of 11.99%. What should your monthly payment be if you would like to pay off your balance in full after two years?  

23.  You make a purchase for $3,501 on your credit card which has an annual interest rate of 17.99%. If you pay the minimum payment of 2% per month (not less than $25), what is your balance after 4.5 years, assuming you make no other purchases with your credit card?

24.  You make a purchase for $2,723 on your credit card which has an annual interest rate of 15.99%. The credit card company offers a minimum payment of 3% per month (not less than $25). How many years will it take your balance to equal $10.00 assuming your make no other purchases with your credit card?