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Assignment 1: Absolute and Relative Quantities

Directions: This assignment should be typed and answers to questions should be in complete sentences, free of grammatical and spelling errors. This assignment will utilize the sort feature in Excel extensively. Start early, so if you have questions, you will have time to ask. All values and percentages should show 2 decimal places, unless otherwise specified.

Open the file on refined petroleum usage (http://faculty.elgin.edu/nscherger/Courses/MTH104/Oil Consumption by Country.xlsx), which contains data on the number of barrels per day used by country.

1. Sort the countries by the barrels used per day, from greatest to least. Copy and paste the first 5 rows of this sorted table into your Word document.

2. Are the values (the daily barrels used) in (1) absolute or relative quantities?

3. Without any knowledge of countries’ petroleum usage, why were the countries that topped the list in (1) not very surprising?

4. Create a column D (don’t forget to give it an appropriate title) with barrels each day per capita (or to say differently, the daily barrels used per person). Leave in decimal form and show 4 decimal places. Now sort the data by column D, from greatest to least, and copy and paste the first 5 rows of this sorted table into your Word document.

5. Are the values you created in column D absolute or relative quantities?

6. If you were writing an article on countries who cultures are highly dependent on refined petroleum products, would it make more sense to focus on countries with the highest barrels used daily (as in the countries listed in 1) or would it make more sense to discuss the countries with the highest daily barrel usage per person (as in the countries listed in 4)? Explain your answer in complete sentences.

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Assignment 2: Absolute and Relative Quantities and Change & Other Percentage Problems

1. We have already looked at the file on poverty in Illinois (http://faculty.elgin.edu/nscherger/Courses/MTH104/Poverty by County in Illinois 2013.xlsx).

In group activity 4, you were asked to if the Illinois State Legislature had $2 million earmarked to help the poor in Illinois, who you thought should get the most money - the counties with the highest percentage of their population in poverty or the counties with the highest number of individuals in poverty. Hopefully you answered that the counties that have the most number of individuals in poverty have the most need, so they deserved the most money.

One way to fairly distribute the money, so that the counties with the most number of people in poverty get the most money, is to determine the percent of the total poverty population that resides in each county (and then give that county that percent of the money)

(a) To do this, create a column D with the number of individuals below poverty for each county (which we did together in class). Be sure to title the column appropriately.

As you did in group activity 4, #2, sort from greatest to least according to the number of individuals below poverty in each county.

Copy and paste the first three rows of this sorted table into your Word document.

(b) Next, find the total number of people in poverty by summing column D (use AutoSum). State this total poverty population.

(c) Now, determine the percent of the total poverty population that resides in each county. To do this, create a column E (with the appropriate title) by computing:

PART (the number in poverty for each state, which are the values you have in the column created in part a) WHOLE (the total poverty population, which you computed in b)*

*While you should be using a cell reference for the numerator, FOR THE DENOMINATOR, TYPE THE ACTUAL NUMBER and do not use a cell reference (because we do NOT want the denominator to change to other cells as we fill the column).

Copy and paste the first 5 rows of this table into your Word document.

(d) Finally, create a column F (with an appropriate title) that will determine how much of the $2 million would go to each county by multiplying the percent of the total poverty population of each county (in column E) by $2 million. Copy and paste the first 5 rows of this sorted table into your Word document.

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2. Open the file on frequent moviegoers (http://faculty.elgin.edu/nscherger/Courses/MTH104/Frequent Movie Goers by Age 2010-14.xlsx). This file contains data from 2010 to 2014 on the number of frequent moviegoers by age group.

(a) Create a column G (don’t forget to give it an appropriate title) with the absolute change in the number of moviegoers from 2011 (note this is 2011 and not 2010) to 2014. Then sort the age groups by this column G (from greatest to least) and copy this sorted table into your Word document.

(b) Create a column H (don’t forget to give it an appropriate title) with the percent change in the number of moviegoers from 2011 to 2014. Now sort by column H (from greatest to least) and copy this sorted table into your Word document.

(c) Complete the following statement:

The 50-59 age group increased its number of frequent moviegoers by _____________________ from 2011 to 2014, which was a percent growth of ________.

Over this same time period, the 60+ age group added even more frequent moviegoers, increasing by _____________________ from 2011 to 2014, but that resulted in the smaller percent growth of ________.

(d) Explain the statement in (c). In other words, why did the 60+ age group gain more moviegoers than the 50-59 age group, but the 60+ group had a smaller percent growth?

NOTE: Exercises 3-7 do not require Excel, but for full credit, you must show all work and correctly label your answer. (Sometimes this label may just be a percent symbol.)

3. According to the MPAA, in 2014, the US/Canada box office brought in 5% less than it did in 2013, when it brought in $10.9 billion. How much did the US/Canada box office bring in in 2014?

4. According to the MPAA, for 18-24 year olds, the average number of 3D movies viewed in 2013 was 1.3 and in 2014 was 1.5. What was the percent increase in the average number of 3D movies viewed for 18-24 year olds from 2013 to 2014?

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5. On the first day of the spring 2015 semester, MTH 112 (College Algebra) had 464 students enrolled and MTH 114 (Trigonometry) had 154 students enrolled.

a) How many times more students were enrolled in MTH 112 than in MTH 114?

b) By what percent was the enrollment in MTH 112 greater than that in MTH 114?

c) By what percent was the enrollment in MTH 114 lesser than that in MTH 112?

6. Facebook stock rose 105.30% from December 3rd 2012 to December 2nd 2013. It then rose 42.76% from December 2nd 2013 to December 1st 2014. By what percentage was the December 1st 2014 price higher than the December 3rd 2012 price? [Hint: The answer is not 148.06%.]

7. The Will County Coroner reported 38 heroin-related deaths in 2013, which is a 322.22% increase in the number of heroin-related deaths that they reported ten years earlier in 2003. How many heroin-related deaths were there in 2003? (Round to the nearest whole number.)

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Assignment 3: Graphical Displays of Data

Directions: This assignment should be typed and answers to questions should be in complete sentences, free of grammatical and spelling errors. Start early, so if you have questions, you will have time to ask.

1. Consider the data in the table below on property crimes in Illinois in 2013, which is available at http://faculty.elgin.edu/nscherger/Courses/MTH104/Property Crime in Illinois 2013.xlsx.

Property Crimes in Illinois in 2013

Type Offenses

Arson 2341

Burglary 57766

Motor Vehicle Theft 20703

Other Theft 210692

Assuming that these are the only four types of property crimes, a pie chart is appropriate.

Thus, make a pie chart to display the data. Include an appropriate title and display category names and percentages. Paste this pie chart into your Word document.

2. Critique the pie chart at the right,

identifying two major violations made.

(One violation should be obvious; A hint

for the second violation is similar

to the assumption we were making in the

creation of the pie chart in #1.)

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3. Open the file http://faculty.elgin.edu/nscherger/Courses/MTH104/Violent Crime in IL by region 1983 and 2013.xlsx, which contains violent crime rate data in Illinois in 1983 and 2013.

(a) Make two single-bar charts that would inform the reader about violent crime rates in Illinois by region in 1983 and 2013. Include appropriate titles and axes labels. Paste these charts into your Word document.

(b) Make a double-bar chart that would inform the reader about violent crime rates in Illinois by region in 1983

and 2013. Include appropriate titles and axes labels AND an appropriately labeled legend. Paste this chart into your Word document.

(c) How do the violent crime rates in 1983 compare with the rates in 2013 in each of the regions? (d) Do you think the double-bar graph or two single-bar graphs are a better way to graphically illustrate the

violent crime rate trends? Explain.

4. The bar chart at the right illustrates how many people had enrolled in “Obamacare” as of March 27th along with how many they (the Obama office) were hoping to have enrolled

by the 31st.

At quick glance, it appears as if they are very short of their goal!

Critique this graph. What, in particular, is causing the (mis)appearance of the dramatic difference in the bars showing the number currently enrolled and their goal for enrollment? Be specific.

FYI – In the interest full disclosure and fairness to Fox news,

they did later release the fairer and more appropriate graph

shown at the right (which should also help you to identify

what was incorrectly done in the first graph).

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5. Consider the following graph, showing US unemployment rates from 2005-2015.

Ignoring all of the minor “ups and downs,” describe the general trends in unemployment, “telling the story over time from left to right,” by filling in each of the following blanks using specific dates (in the form of month-year), approximate values (so percentages) from the graph, and vocabulary (such increasing, decreasing, and absolute/relative minimum and maximum).

The US unemployment rate______________ from Feb-05 to the _______________ _______________ of about

________% in ____________. The US unemployment rate then____________over from _________to_________,

reaching the _______________ _______________ of about ________% in___________. After that, the US

unemployment rate _______________ from ________to________, ending at about _________%.

6. Open the file http://faculty.elgin.edu/nscherger/Courses/MTH104/Heroin Deaths 1999-2013.xlsx, which contains data on national overdose deaths from heroin from 1999 to 2013.

(a) Make a scatterplot (select an option under scatterplot that still shows the data points, so the first or second option) of the data (be sure to include a title and appropriate labels for the x and y axes) and paste it into your Word document.

(b) Refer to your graph in (a) and describe each of the intervals below as increasing slowly, increasing quickly, relatively stable, decreasing slowly, or decreasing quickly.

(a) 1999-2006 (b) 2006-2009 (c) 2010-2013

Graphs are like jokes: If you have to explain them, they have failed. -Sally Bigwood

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Assignment 4: Measures of Average and Spread

Directions: This assignment should be typed and answers to questions should be in complete sentences, free of grammatical and spelling errors. Start early, so if you have questions, you will have time to ask.

1. Open the file http://faculty.elgin.edu/nscherger/Courses/MTH104/Downtime.xls. This manufacturer of minicomputer systems is interested in improving its customer support services. As a first step, its marketing department has been charged with the responsibility of summarizing the extent of customer problems in terms of system downtime. The most recent 40 customers were surveyed to determine the amount of downtime they had experienced during the previous month. The file contains the customer client number and their downtime.

(a) Find the mean downtime.

(b) Find the median downtime.

(c) If you worked in marketing for this company (so, your job is to promote your company and to try to make

them look as good as possible) and were going to report an average downtime, which measure of average (mean or median) would you us? Explain.

(d) Find the five number summary. (e) Outliers would be any data less than what value?

Or data greater than what value? (f) Using the guidelines in (e), list any outliers.

2. Open the file http://faculty.elgin.edu/nscherger/Courses/MTH104/Age At Inauguration.xlsx.

(a) Find the mean age at inauguration.

(b) Find the median age at inauguration.

(c) Find the average spread of the ages about the mean. (You should be using the statistic here that is interpreted as “the average spread about the mean.”)

(d) Donald Trump was 70 at inauguration. About how many standard deviations is he be above the mean? 3. Read the comic. To help explain the joke, suppose there are 5 salaries in Mr. Stingy’s

company: 4 workers and himself. Give an example of what all 5 salaries

could be for the median salary to be less than $40,000 and mean salary to be over $90,000?

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4. Suppose that the five-number summary for salaries of full-time teachers in school districts A and B are given below. Determine the following, if possible.

Minimum: $37,500 1st Quartile: $45,300 Median: $53,400 3rd Quartile: $67,120 Maximum: $92,900

(a) What percentage of teachers in district A make less than $53,400? (b) What percentage of teachers in district B make between $42,200 and $80,120?

(c) What percentage of teachers in district B make less than $50,000?

(d) If there are 108 teachers in district A, how many teachers make more than $67,120? (e) Determine the ranges of salaries for each school district. (f) Determine the interquartile ranges of salaries in each school district.

(h) While you cannot compute the standard deviations exactly without the entire data set, which district do you

think would have the larger standard deviation? Explain.

Minimum: $38,500 1st Quartile: $42,200 Median: $61,400 3rd Quartile: $80,120 Maximum: $102,200

School District A: School District B:

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Data Values:

Cumulative Percentiles:

Assignment 5: Normal Distribution and Correlation & Causation

Directions: This assignment should be typed and answers to questions should be in complete sentences, free of grammatical and spelling errors. Start early, so if you have questions, you will have time to ask.

For 1-3, ACT scores are normally distributed with a mean of 21 and a standard deviation of 3. 1. Fill in the boxes on the normal curve below.

2. Using the completed table above (NOT EXCEL), answer the following questions, if possible.

(a) What ACT score is in the 2.5th percentile? (b) What percent of ACT scores is below 18? (c) What ACT score is in the 80th percentile? (e) What percent of ACT scores are over 24? (f) In a group of 400 students, how many would you expect to score less than 27?

3. Now use EXCEL to answer the questions that follow.

(a) A student is randomly selected. What is the probability that his/her ACT score is below 20? (b) What ACT score is in the 75th percentile? (d) What percent of ACT scores are between 18 and 22? (e) What percent of ACT scores are over 24? (f) To qualify for a scholarship, you need to be in the top 30% of all ACT scores. What ACT score

would that be?

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4. Determine if the following data sets would have a positive correlation, a negative correlation, or no correlation (so, correlation close to 0). (Note: This exercise is referring to the correlation coefficient, r.)

a.

b.

5. Open the file http://faculty.elgin.edu/nscherger/Courses/MTH104/Life Expectancy and Percent Urban by Country.xlsx. The file contains data on countries’ life expectancy and the percent of their population that is urban.

a. Obtain a scatterplot of the countries’ life expectancy and the percent of their population that is urban. Include an appropriate title and axes labels. Copy and paste this plot into your Word document.

b. Does it look like there will be a positive correlation, a negative correlation, or no correlation (so, correlation close to 0)?

c. Determine the actual correlation coefficient, r, between countries’ life expectancy and the percent of their population that is urban.

d. According to the standards in our notes, how would we classify this correlation?

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6. The following statements indicate a real correlation exists between two variables. Do you think that these show a reasonable case for causation as well? If you say yes, explain your answer. If you say no, then give at least one possible “lurking” or “confounding” variable.

Start all your responses with ONE of the following:

Yes, I think there is a reasonable case for causation, because…

OR

No, I do not think there is a reasonable case for causation. The most likely lurking/confounding variable is….

a. A health club went under new management after the start of the year. During their first month under new management, the sales of new memberships soared!

Did the new management cause the increase in sales?

b. There is a negative correlation between amount children’s screen time (television, video games, phones, computers, tablets, etc..) and length of their attention span. (That is, the greater their screen time, the shorter their attention span.)

Does screen time cause reduced attention span?

Carl Friedrich Gauss, who is most commonly credited with the bell-shaped curve, appeared on the German ten-mark banknote from 1989 to the end of 2001 in his honor.

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x y

3 -6

7 -1

11 4

15 9

x y

0 0

2 5

4 10

8 15

Assignment 6: Linear Relationships and Modeling

Directions: This assignment should be typed and answers to questions should be in complete sentences, free of grammatical and spelling errors. Start early, so if you have questions, you will have time to ask.

1. Determine if the following relationships are linear or non-linear. If they are linear, determine the linear equation. If they are not linear, explain why not.

a. b.

2. Open the data file http://faculty.elgin.edu/nscherger/Courses/MTH104/Fundraising by Political Party 1987-2012.xlsx, which contains fundraising by political party from 1987-2012.

a. Create a new column D for years, where 0 corresponds to the beginning of 1985 (so, your first values should be 2, 4, …). Then, create a new column E that is the sum of the spending by Democrats and Republicans. Copy and paste this table into your Word document.

b. Make a scatterplot of the data, including a title and axes labels. Observe that while there are minor fluctuations to the data, there is a general upward trend that could be modeled by a linear function. Thus, add a linear trendline to your plot, including the equation and the R2 value. Also, forecast forward by 5 units. Copy and paste this plot into in your Word document.

c. Use this linear model (equation) to predict the amount of spending in 2015-16. Show work and label your answer.

d. Does this prediction seem reasonable?

3. Open the data file http://faculty.elgin.edu/nscherger/Courses/MTH104/Elgin Population 1860-2010.xlsx, which contains Elgin’s population by 10 year increments from 1860-2010.

a. Create a new column C for years, where 0 corresponds to 1850 (so, your first value should be 10). Then, it will be easiest to just recopy the population data from column B into column D. Copy and paste this table into your Word document.

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b. Make a scatterplot of the data, including a title and axes labels. Then, add a linear trendline to your plot, including the equation and the R2 value. Also, forecast forward by 10 units. Copy and paste this plot into in your Word document.

c. Compare the overall fit of the model in both #2 (political fundraising) and with this model in #3 (Elgin population), incorporating the R2 values into your answer.

d. Use this linear model (equation) to predict the Elgin Population in 2020. Show work and label your answer.

e. Does this prediction seem reasonable? Explain.

Important Observation: Even though the R2 was higher in this linear model than in the linear model in #2, the prediction in #2c made more practical sense with the data than did this prediction in #2d.

Thus, once again, we are seeing that we cannot rely on R2 alone to determine the predictive value of a model.

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Assignment 7: Non-Linear Relationships and Modeling

Directions: This assignment should be typed and answers to questions should be in complete sentences, free of grammatical and spelling errors. Start early, so if you have questions, you will have time to ask.

1. The graph below is a plot of a 40-year old woman’s weight over her lifetime, using weights from various doctor’s office visits. Answer the questions below.

a. What is the independent variable?

b. What is the dependent variable?

c. What is the domain?

d. What is the range?

2. Open the data file http://faculty.elgin.edu/nscherger/Courses/MTH104/Number of Motorcycles 1960-2012.xlsx, which contains data on the number of motorcycles in the US from 1960-2012.

A. Create a new column C for years, where 0 corresponds to 1960 (so the first value should be 0), but be careful here, because the years do not always go up by the same increments. Then, copy the number of motorcycles data into column D. Copy and paste this table into your Word document.

B. Make a scatterplot of the data, including a title and axes labels. Copy and paste this plot into your Word

document.

C. According to the guidelines in the middle of page 67, what type of equation would make the most sense to fit when looking at this data?

D. Perform a cubic (degree 3) regression, including the equation and the R2 value. Also, forecast forward by 4

years. Copy and paste this plot into in your Word document.

E. (i) Use the cubic regression equation to interpolate the number of motorcycles in 1996. Show work and label your answer.

(ii) Does this seem reasonable? Explain. (Hint: Look at the actual data near 1996.)

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F. In an effort to get a model that is a better fit to the data, perform a degree 5 polynomial regression to the data. Include the equation and the R2 value and forecast forward by 4 years. Copy and paste this plot into your Word document.

G. (i) Use the degree 5 regression equation to interpolate the number of motorcycles in 1996. Show work and label your answer.

(ii) Does this seem reasonable? Explain.

H. Compare the overall fit of the degree 3 model with the degree 5 model, incorporating the R2 values into your answer.

I. (i) Use the cubic (degree 3) regression equation to extrapolate the number of motorcycles in 2016. Show

work and label your answer. (ii) Use the degree 5 equation to extrapolate to extrapolate the number of motorcycles in 2016. Show work

and label your answer.

(iii) Which model (degree 3 or degree 5) seems more reasonable for 2016? (Hint: Look at the general trend of the data itself.)

(iv) Is your answer for (iii) the same model you said had a better overall fit (in H)?

SO, NOTE:

What occurred here is why it is so important to always think about these regression equations and their predictions both mathematically and logically.

Sometimes the model with the better overall fit and higher R2 is

NOT the best choice for predictive purposes.

We must always look at HOW we are using a model to decide what model is best.

Mathematical modeling is about rules - the rules of reality. What distinguishes a mathematical model from, say, a poem, a song, a portrait or any other kind of 'model', is that the mathematical model is an image or picture of reality painted

with logical symbols instead of with words, sounds or watercolors. -John Casti

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Assignment 8: Exponential Relationships

Directions: This assignment should be typed and answers to questions should be in complete sentences, free of grammatical and spelling errors. Start early, so if you have questions, you will have time to ask.

1. Determine if the following relationships are linear, exponential, or neither. If linear, determine the slope; If exponential, give the multiplicative (growth or decay) factor.

a. b.

2. The drug valium is eliminated from the bloodstream at a rate of 1.9% per hour. A patient receives an initial does of 20 milligrams.

a. Write out the exponential model (equation). (𝑦 = 𝐴𝑏𝑥)

b. Use your model to determine how much valium is in the patient's blood 12 hours later. Show work and label your answer.

c. Use Excel to determine how much valium is in the patient’s blood 12 hours later.

Set up 2 columns: time (starting at 0) and amount of valium (starting at 20). Copy the table up to and including the row you need to determine your answer into your Word document. (Make sure you got the same answer as in b.)

d. Use your Excel spreadsheet to determine what the half-life of valium in the human body? (Recall: The half-life is

the time it takes for the amount to reach 50% of the original amount.)

3. The burning of fossil fuels (oil, coal, natural gas) releases carbon dioxide into the atmosphere. Carbon dioxide is known as a greenhouse gas because it tends to trap heat in the atmosphere, causing global warming.

In 1995, the United States emitted about 1.4 billion tons of carbon (as carbon dioxide) into the atmosphere and at that time, were increasing at 1.3% a year. China was second largest contributor, emitting 850 million tons and at that time, were increasing at 4% a year. Assuming these growth rates continued, use Excel to determine the year when China will exceed US in carbon emissions.

Set up three columns: date, US emissions, China emissions and extend the table as far as needed to determine your answer. Copy the first two and last two rows of your table into your Word document and state your final answer.

x y

3 2

6 5

9 12.5

12 31.25

x y

1 2

2 4

3 16

4 96

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4. In order to understand the prehistory of the Hawaiian island of Lana'i better, anthropologists Maria Sweeney, Melinda Allen, and Boyd Dixon used radiocarbon dating on charcoal found in an ancient dwelling site, the Kaunolu Village National Historic Landmark, the largest archeological complex on the island.

In one of their samples, they found that approximately 94% of the original carbon 14 remained. Using the fact that Carbon 14 decays by 1.202% every 100 years, determine the approximate age of this sample.

In your Word document, paste the Excel table you made to come up with your answer.

5. A student strained her knee in an intramural volleyball game. Her doctor prescribed an anti-inflammatory drug to reduce the swelling. She is to take a 440 mg tablet of the drug every 8 hours for 7 days. Her kidneys filter, or remove 60% of the drug from her body every 8 hours.

a. Show that after 8 hours, just after she has taken her second tablet, the student has 616 mg of the drug in her system.

b. Create an Excel data table which will determine the amount of drug in the student's body during the course of the 7 days she is taking the drug. The top of your table might look like the following:

Time (hours) Amount filtered by kidneys (mg)

Amount left after filtering by kidneys (mg)

New dose (mg) Total amount in body

(mg)

0 0 0 440 440

8 =E2*.60 =E2-B3 440 =C3+D3

⋮ ⋮ ⋮ ⋮ ⋮

Include the table with information for the 7 days in your Word document.

c. What is the maximum amount of drug in the student's body over the course of the 7 days?

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d. Make a scatterplot of the total amount of drug in the student's body (so, you will need to highlight the first and last columns only) over just the first 3 days. As always, include a title and axes labels. Paste this graph into your Word document.

e. Describe the graph.

f. Create a new table OR modify and extend the current table to show the amount of drug remaining in the student's body for three days after she stops taking the drug (that is, for days 8, 9 and 10). Remember that her kidneys flush out 60% of the drug every 8 hours. Paste this table into your Word document.

g. Is the data in the table in (f) linear or exponential? Determine this as you did in #1. Copy and paste the Excel table that shows that the data is linear or exponential and state your final answer. If it is linear, state the slope. If it is exponential, state the growth or decay rate.

The mathematics of uncontrolled growth are frightening. A single cell of the bacterium E. coli would, under ideal circumstances, divide every twenty minutes. That is not particularly disturbing until you think about it,

but the fact is that bacteria multiply geometrically: one becomes two, two become four, four become eight, and so on. In this way it can be shown that in a single day, one cell of E. coli could produce a super-colony equal in size

and weight to the entire planet Earth.

Michael Crichton (1969) The Andromeda Strain, Dell, N.Y. p247

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Assignment 9: Consumer Price Index

Directions: This assignment should be typed and answers to questions should be in complete sentences, free of grammatical and spelling errors. Start early, so if you have questions, you will have time to ask.

1. You and your grandfather are engaged in a conversation about the hourly wages you earned in your first job. Your grandfather insists that you don’t know how good you have it, because in your first job in 2012, you made $8.25/hour and your grandfather only made $1/hour at his first job in 1956. What is your grandfather’s hourly wage in constant 2012 dollars? Who actually was making a better wage for their time – you or your grandfather?

2. In 1950 the median household income was $3,319, while the average Major League baseball player salary was $13,228. In 2012 the median household income was $51,371, while the average Major League baseball player was $3.44 million.

a. (i) Convert the 1950 median household income into constant 2012 dollars.

(ii) Was the median household income better in 1950 or in 2012, relative to the time?

b. (i) Convert the 1950 average Major League baseball player salary into constant 2012 dollars.

(ii) Was the average Major League baseball player salary better in 1950 or in 2012, relative to the time?

c. (i) By what percent higher is the actual 2012 median household income over the 1950 median household income in 2012 dollars?

(i) By what percent higher is the actual 2012 average Major League baseball player salary over the

1950 Major League baseball player salary in 2012 dollars?

(ii) Thus, did the median household income or the average Major League baseball player salary increase faster?

3. The movie industry has been accused of dramatically over-inflating the cost of tickets.

a. Open the file http://faculty.elgin.edu/nscherger/Courses/MTH104/Movie Ticket Prices 1983-2014.xlsx and create a scatterplot of the data, including appropriate axes labels and a title (remember…this data is in what we call nominal dollars). Paste this graph into your Word document.

b. What is the general impression of the graph?

c. Now suppose that you work for the movie industry and have just seen the graph that you created in part (a) in a newspaper article in which the industry was criticized for over-inflating the cost of tickets. Remembering what you learned about CPI from your liberal arts mathematics course, you decide to submit to the newspaper a more accurate graph of the cost of movie ticket prices in CONSTANT 2014 DOLLARS.

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First, in column C, paste the CPI values (at http://faculty.elgin.edu/nscherger/Courses/MTH104/CPI.xlsx) for the corresponding years. Then, in column D perform the necessary operations to fill this column with the ticket prices in constant 2014 dollars. Copy and paste this table into your Word document.

d. Now, create a scatterplot of movie ticket prices in constant 2014 dollars. Include axes labels and a title. Paste this graph into your Word document. Observe how its general impression is very different than that of the first graph.

e. Keeping in mind that movie prices in nominal dollars (as shown on your first graph) were generally increasing, answer the following questions regarding the interpretation of the second graph, in constant dollars.

(i) What can you say about regions of the constant dollars graph, such as from 1983-1988, that are increasing? Specifically, is the price of movie tickets increasing less than, about the same as, or more than what other goods and services were increasing during these times?

(ii) What can you say about regions of the constant dollars graph, such as from 1990-1994, that are decreasing? Specifically, is the price of movie tickets increasing less than, about the same as, or more than what other goods and services were increasing during these times?

(iii) What can you say about regions of the constant dollars graph, such as from 1994-1998, that are

relatively constant? Specifically, is the price of movie tickets increasing less than, about the same as, or more than what other goods and services were increasing during these times?

4. Recall that the inflation rate is defined to be the percentage change in the annual CPI. For example, the CPI in 1998 was 163.0 while the CPI in 1999 was 166.6. The inflation rate for 1999 was therefore (166.6-163.0)/163.0 or 2.2%. The inflation rate is important for many reasons. High inflation means that the money we earn and have saved up in the past is worth less. Interest rates for houses, cars, and credit cards rise if the inflation rate is high. For a variety of reasons, stock prices tend to fall even on hints of higher inflation. Increases for many government entitlement programs are tied to the inflation rate.

a. Again, open the file http://faculty.elgin.edu/nscherger/Courses/MTH104/CPI.xlsx. Add a new column to the table that contains the annual inflation for each year. Paste the resulting table only for the last 40 years 1974-2014 into your Word document.

b. Make a scatterplot (choose the 2nd option with the connecting lines) of the inflation rate from 1974 to 2014. Paste it in your Word document.

c. Although there are always fluctuations, how would you generally compare the inflation rates of the 1970s and 1980s with the inflation rates of the 1990s and 2000s?

If I had to populate an asylum with people certified insane, I’d just pick ‘em from all those who claim to understand inflation.

-Will Rogers

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Assignment 10: Savings Accounts and APR vs APY

Directions: This assignment should be typed and answers to questions should be in complete sentences, free of grammatical and spelling errors. Start early, so if you have questions, you will have time to ask.

1. a. If a bank account has an APR of 5.3%, where interest is compounded monthly, make an Excel spreadsheet (using

any principal amount) and determine how long it would take the bank account to double. Copy the first three and last three rows of your Excel table in your Word document.

b. Use the Rule of 70 to approximate its doubling time. Show work. (Hint: You cannot use the 5.3% here, because

the APR is not the actual percent of growth over 1 year when interest is compounded monthly. You will need to find the APY.) Note: Your answers to a and b should be very close, but may not necessarily be exactly the same.

2. Suppose that you invest $1500 at an annual percentage rate of 6.0%, compounded quarterly.

a. What is your account balance after one year? Create and copy an Excel table into your Word document.

b. What is your account balance after 10 years? Create and copy only the row from your Excel table where you determined your answer.

c. What is the annual percentage yield for this account? Utilize a couple of the cell entries from your Excel table to

compute the APY, showing your work. 3. You still wish to deposit the same $1500 as in number 2, but now you found an investment that is offering an annual

percentage rate of 6.4%, compounded semi-annually.

a. What is your account balance after one year? Find without making an Excel spreadsheet (so, using the appropriate Excel function).

b. What is the annual percentage yield for this account? Find without making an Excel spreadsheet (so, using the appropriate Excel function)

c. Which account would you choose (#2 or #3)? Explain your answer.

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4. Suppose you had a choice between two investments. The first compounds interest annually at an annual percentage rate of 3.63%. The second compounds interest monthly at an annual percentage rate 3.60%. Use the APY to determine the higher yielding investment.

5. How much would you need to invest now (as a one-time principal deposit) in order to have $4,000 for a down payment on a new car in 6 years, if the savings plan has an APR of 7.25%, where interest is compounded monthly? Find without making an Excel spreadsheet (so, using the appropriate Excel functions; hint: you are planning for a goal…).

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Assignment 11: Savings Accounts and Planning for Retirement

Directions: This assignment should be typed and answers to questions should be in complete sentences, free of grammatical and spelling errors. Start early, so if you have questions, you will have time to ask.

1. Your Retirement: Plan A - Starting Early

a. You begin to deposit $200 dollars a month, every month for 36 years, into an account that pays 6.2% interest compounded monthly. How much money will be in the account when you retire? Make an Excel spreadsheet to solve this problem. Copy only the first three rows and the last three rows into your Word document.

b. How much money did you end actually deposit?

2. Your Retirement: Plan B - Waiting Until Middle Age

a. Realizing that you will be saving for half as long, you decide to double your monthly deposits, hoping that this

will “even things out.” So, you deposit $400 a month, every month for 18 years, into an account that pays 6.2% interest compounded monthly. How much money will be in the account when you retire? Did you end up with about the same amount as in plan A (exercise 8)? (You may use an Excel function exclusively here and not set up a spreadsheet.)

b. How much money did you actually deposit?

3. Your Retirement: Plan C - Starting Early and Planning for a Goal

a. Upon retirement (40 years from now) you want to have enough money to withdraw $2000 a month for a period

of 25 years. How much money do you need to save if you were to withdraw this total amount as one lump sum when you retire? (Note: In reality, you would not be withdraw this money in one lump sum and it would continue to earn interest, even after you start withdrawing it; however, for purposes of this problem, we are going to simplify the scenario and pretend that we would be withdrawing this one large sum when we retire.)

b. You plan to deposit money every month for 40 years into an account that pays 6.2%, compounded monthly. What monthly deposit must you make to achieve the amount of money determined in the answer to Part a? (Hint: You are planning for a goal…)

c. How much money did you actually deposit?

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4. Your Retirement: Plan D, Waiting Until Middle Age and Planning for a Goal

a. Use the same amount of money from plan C (in 8a), what monthly deposit must you make to achieve this amount of money in 20 years at 6.2% compounded monthly? (Hint: You are planning for a goal…) b. How much money did you actually deposit?

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Assignment 12: Loans

Directions: This assignment should be typed and answers to questions should be in complete sentences, free of grammatical and spelling errors. Start early, so if you have questions, you will have time to ask.

1. You find a car you really want that is priced at $14,000. The car dealership says they will drop the price to $12,000, if you take their financing. They offer you 6.75% for 4 years. You tell them you will think about it.

(a) Having taken liberal arts mathematics, you use the appropriate formula in Excel to determine the monthly

payment. What is that monthly payment? (b) Construct a table in Excel with columns for the month, the balance at the beginning of the month, the

monthly payment, the interest for the month, and the balance at the end of the month, and verify that the loan is paid off in 4 years. Copy the first two and last two rows of the table into your Word document.

(c) You go back to the car dealership and say you would like to take the deal. Unfortunately, when you sit

down to work out the details, they tell you that the monthly payment will be $317.50. You tell the dealership that you thought that your payment was going to be less than that (the value you got in part a) and you ask them how they got their number. They tell you "Simple Interest". The dealer tells you, rather rudely, that you must have done something wrong and asks you if you can afford the $317.50. You tell him yes, but that you’d like to think about it.

You’re a little unsure as to what the dealership is doing, so you visit your former liberal arts mathematics teacher and we discover that they are computing “Simple Interest” on the original principal and not on the remaining balance each month. That is, instead of the interest amounts decreasing over time (as shown in your table from part b), they consistently used the monthly interest, computed from the original $12,000, as indicated below:

Month Beginning Balance Monthly Payment Interest Charge Ending Balance

1 12000 317.5 67.5 11750 2 11750 317.5 67.5 11500 3 11500 317.5 67.5 11250 4 11250 317.5 67.5 11000 5 11000 317.5 67.5 10750 6 10750 317.5 67.5 10500 7 10500 317.5 67.5 10250 8 10250 317.5 67.5 10000 9 10000 317.5 67.5 9750 10 9750 317.5 67.5 9500 11 9500 317.5 67.5 9250 12 9250 317.5 67.5 9000 13 9000 317.5 67.5 8750 14 8750 317.5 67.5 8500 15 8500 317.5 67.5 8250 16 8250 317.5 67.5 8000

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17 8000 317.5 67.5 7750 18 7750 317.5 67.5 7500 19 7500 317.5 67.5 7250 20 7250 317.5 67.5 7000 21 7000 317.5 67.5 6750 22 6750 317.5 67.5 6500 23 6500 317.5 67.5 6250 24 6250 317.5 67.5 6000 25 6000 317.5 67.5 5750 26 5750 317.5 67.5 5500 27 5500 317.5 67.5 5250 28 5250 317.5 67.5 5000 29 5000 317.5 67.5 4750 30 4750 317.5 67.5 4500 31 4500 317.5 67.5 4250 32 4250 317.5 67.5 4000 33 4000 317.5 67.5 3750 34 3750 317.5 67.5 3500 35 3500 317.5 67.5 3250 36 3250 317.5 67.5 3000 37 3000 317.5 67.5 2750 38 2750 317.5 67.5 2500 39 2500 317.5 67.5 2250 40 2250 317.5 67.5 2000 41 2000 317.5 67.5 1750 42 1750 317.5 67.5 1500 43 1500 317.5 67.5 1250 44 1250 317.5 67.5 1000 45 1000 317.5 67.5 750 46 750 317.5 67.5 500 47 500 317.5 67.5 250 48 250 317.5 67.5 0

Over the course of the entire loan, their method of calculating interest would have cost you how much more?

(d) Realizing that they have been caught in a deceptive (although not illegal) practice, the car dealership says it must have been a computer glitch. To make up for the mistake, they offer you financing of 5.75% for 4 years (now calculated accurately, as you did). (i) What will your monthly payment now be?

(ii) How much will you pay in total over the course of the loan?

(iii) How much will you pay in interest over the course of the loan?

Note: This problem was inspired by the true events of a fellow mathematics instructor.

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2. Assume that you have a balance of $1500 on a credit card that carries an annual percentage rate of 18%.

(a) You pay the minimum payment of 2.5% per month (not less than $20), and make no additional purchases on your card. Construct a table in Excel with columns for the month, the balance at the beginning of the month, the monthly payment, the interest for the month, and the balance at the end of the month.

How long will it take you to pay off the $1500 if you only make the minimum payment? Copy the first two and last two rows of your table into your Word document.

(b) How much did you pay in total?

(c) Realizing that you should make more than the minimum monthly payment, you decide to pay $100 a month. How long does it take you to pay off the balance now?

(d) How much did you pay in total? (e) Now suppose that while you are making $100 monthly payments, you start charging an additional $50 per

month. Assume that this charge is made at the end of the month and interest is calculated on the balance before the charge is added. Make a table that shows month, beginning balance, payment, interest, charge amount, and end balance.

How long will it take to pay off your credit card now? Copy the first two and last two rows of your table into your Word document.

(f) Repeat exercise (e), but assume you only make monthly payments of $80, how long will it take to pay off the credit card debt?

3. You are buying a townhouse that is $210,000. You have two different plans you are deciding between.

Bank A: 30-year 6.6% fixed-rate loan with closing costs of $1000 with 1 point. Bank B: 30-year 6.9% fixed-rate loan with closing costs of $2000 with no points.

(a) You are going to put 20% down, so you need a loan for how much?

(b) How much will you pay per month with bank A? (c) How much will you pay in total with bank A? (Total of all payments, closing costs, and points) Show work. (d) How much will you pay per month with bank B?

(e) How much will you pay in total with bank B? (Total of all payments, closing costs, and points) Show work.

(f) Which bank will you choose?

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4. You are buying a house that is $300,000 and will be financing $240,000. You have a 30-year 6% fixed-rate loan.

(a) How much will you pay per month?

(b) How much will you pay over the course of your entire loan?

(c) Now suppose that you decide that you can afford an extra $50 a week to put towards your house, and you start making payments that are $200 more than the original monthly payment (from part a). Make a table that shows month, beginning balance, payment, interest, and end balance.

How long will it take you to pay off your house if you pay an additional $200 each month? Copy the first two and last two rows of your table into your Word document.

(d) How much will you pay over the course of your entire loan (paying the additional $200 / month)?

(e) How much will you save over the course of your entire loan (paying the additional $200 / month)?