ISP 120 Week 4

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ISP 120 Week 4

• Absolute vs. Relative Quantities

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Homework/Activities

• All group members must participate in each
  problem on activities from now on
• All group members MUST sign the activity
• You MUST write in complete sentences which
  includes a capital letter at the beginning of the
  sentence and a period at the end of the sentence
• Show your work or else you will get no credit if
  the problem is wrong

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Activity 2 - 5

• 5.  World oil production was 518 million tons in
  1950.  Between 1950 and 1972, production
  increased at a rate of 7 per year.  World oil
  production in 1998 was approximately 3300 million
  tons.
• a.  Using the information above, estimate the
  world oil production in 1972?
• y 518(1.07)222294.95 million tons of oil

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• b.  Using the result of part a, determine how
  much oil would have been produced in 1998 if
  growth in production had continued at a rate of
  7 between 1972 and 1998.  Compare this result to
  the actual 1998 figure given above.
• y 518(1.07)48 13,327.57 million tons
• OR
• y 2294.95(1.07)26 13,327.58 million tons
• These results are way more than the actual figure

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• c.  Using the result of part a, determine how
  much oil would have been produced in 1998 if
  growth in production had proceeded at a rate of
  3 between 1972 and 1998.  Compare this result to
  the actual 1998 figure given above.
• y 2294.95(1.03)26 4949.27 million tons
• This is still more than the actual figure
• d.  Using your answer from part a, estimate the
  actual annual growth rate in world oil production
  between 1972 and 1998.
• We know that it has to be less than 2 from c.
  So plug in values for r
• 3300 2295.94(1r)26
• r is approximately 1.4 or 1.5

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Activity 3

• 1. Beryllium-11 is a radioactive isotope of the
  alkaline metal Beryllium.  Beryllium-11 decays at
  a rate of 4.9 every second. 
• a) Assuming you started with 100, what percent
  of the beryllium-11 would be remaining after 10
  seconds? Either copy and paste the table or show
  the equation used to answer the question. 
• y 100(1-.049)10 .6051 60.51

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• b) How long would it take for half of the
  beryllium-11 to decay?  This time is called the
  half life.  (Use the "solve using logs" process
  to answer the question)  Show your work. 
• 50100(1-.049)x must divide by 100 first!!
• 50/100 (.951)x
• log(.5) log(.951)x xlog(.951)
• x log(.5)/log(.951) 13.8 seconds

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• 2. Some of the most famous Cro-Magnon cave
  paintings are located in Lascaux, France. On the
  right is an image from Lascaux. Charcoal found in
  the cave has approximately 14 of the carbon 14
  found in living wood. Carbon 14 decays
  approximately 1.202 every 100 years.
• a) Make a table in Excel that has in column A 
  years  in increments of 100 and in column B the
  percent of Carbon 14 remaining.  Use the table to
  approximate the age of the paintings. 

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. . . . .
. . . . .
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• b)  Now answer the same question using logs
  instead of a table.   Here you will need to
  define x as the number of 100 year
  increments--meaning x3 would translate to 300
  years.  Show your work.
• 14 100(1-.01202)x must divide by 100
  first!!
• log(.14) log(.98798)x xlog(.98798)
• x 162.59
• Therefore, it would take 162.59100 16,259
  years to have only 14 Carbon 14 remaining.

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• 3.  Rock samples brought back from the moon by
  Apollo astronauts have approximately 58 of the
  original amount of Uranium 238 present. Uranium
  decays at a rate of approximately 7.41 every 500
  million years. 
• a) Make a table in Excel that has in column A
  million years after formation in increments of
  500 and in column B the percent of Uranium 238
  remaining.  Approximate how old the rocks are

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• b)  Now answer the same question using logs
  instead of a table.  You will need to define x in
  the formula as the number of 500 million year
  increments--meaning if you get x2, that would
  translate to 1000 million years.  Round your
  answer to the nearest million years.   Show your
  work
• 58 100(1-.0741)x must divide by 100 first!!
• log(.58) xlog(.9259)
• x 7.075 ? 7.075 500 3537.5 years
• c)  Use logs to find how many years since
  formation until there is only 20 of the Uranium
  remaining.  Show your work. 
• 20 100(1-.0741)x must divide by 100 first!!
• log(.2) xlog(.9259)
• x 20.9 ? 20.9 500 10450.0 years

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Assignment 2 - 1

• a.  A ticket to the Lovehammers concert at Metro
  was marked up by 95.5.  If the original price
  was 10, what was the final price including fees
  (the marked up price)?
• The ticket cost 10(1.995) 19.55.
• b.  On August 16, 2005, one share of Telephone
  Data Systems Inc. stock cost 42.90.  On
  September 2, 2005, the stock closed 5 lower than
  the price on August 16th.  What was the cost of
  one share of Telephone Data Systems Inc. stock
  on September 2nd?
• One share cost 42.90(1-.05) 40.755 40.76.

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2

• 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. China was second largest contributor,
  emitting 850 million tons.  US emissions were
  increasing at 1.3 a year, while Chinese
  emissions were increasing at 4 a year. Assuming
  these growth rates continued determine the year
  when China will exceed US in carbon emissions.
• US emissions 1400(10.013)x
• Chinas emissions 850(10.04)x

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• 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 the this
  sample.
• 94100(1-.01202)x

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• Chicken Bacteria  The information given below
  was found on the label of a package of Chicken.

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• a.  By using the percentage change formula above,
  show that the above data is exponential.  What is
  the percentage increase in bacteria each day?
• Percent change 15 15100 1500 per day

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• b.  It is also noted on the label that at 40º F,
  the bacteria double in number every 6 hours. 
  Make a new table showing the bacteria count every
  6 hours. 
• c.  What is the percentage increase in bacteria
  every six hours?

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5

• In 1980, the number of African elephants was
  1,200,000 but that number was decreasing 5.25 a
  year. 
• a. How many African elephants were there in
  1988?  Show either your table or your
  calculation.
• y 1200000(1-.0525)8 779497.9819
• There were approximately 779,498 elephants in
  1988.

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• b. How many years did it take for the population
  to reach 1/2 of what it was originally?  Use logs
  and round answer to the nearest tenth.
• 600000 1200000(1-.0525)x (must divide by
  1200000 first!!)
• 600000/1200000 .9475x
• log(.5) xlog(.9475)
• x log(.5)/log(.9475) 12.85311
• It took 12.9 years for the population to reach
  600,000.

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• In 2005, the 2004 populations and projected
  population rates were released for Russia and
  Nigeria.  The population of the Russia in 2004
  was 143.8 million the population of Nigeria was
  129 million.  Russia is decreasing in population
  by approximately 0.7 annually the population of
  Nigeria is growing at 2.4.   Using logs and
  letting x be the number of years since 2004,
  answer the following questions.  Round both
  answers to the nearest tenth.
• Russias Population y 143.8(1-.007)x
• Nigerias Population y 129(1.024)x

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• a.  How long, at the above rates, will it take
  for the population of Nigeria to double? 
• 258 129(1.024)x
• x 29.22634
• It will take 29.2 years for Nigerias population
  to double.
• b.  How long, at the above rates, will it take
  for the population of Russia to reach 125
  million?
• 125 143.8(1-.007)x
• x 19.94554
• It will take 19.9 years for Russias population
  to reach 125 million people.
•  

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Week 4 Absolute vs. Relative Quantities and
Percentage Of

• Absolute Quantities
• Relative Quantities
• Percentage Of
• The Mapping Tool
• Worksheet 4
• Activities 5 6

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Absolute and Relative Quantities

• There are two ways to measure numerical data
  particularly if the goal is to measure the least
  and greatest occurrence of some quantifiable
  variable

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Absolute Quantities

• The absolute quantity of a quantifiable variable
  is a measure of the absolute occurrence of the
  variable
• It is a sheer number
• http//qrc.depaul.edu/Excel_Files/StateLotteries20
  00.xls

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Relative Quantities

• The relative quantity of a quantifiable variable
  is a measure of the absolute occurrence of the
  variable in relation to some other quantifiable
  variable
• For example in the previous spreadsheet, one
  could calculate ticket sales per person by
  dividing absolute sales by the population of the
  state

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Another Example of Absolute/Relative Quantities

• South Africa HIV - NY Times
• http//qrc.depaul.edu/Excel_Files/HIV_Adults_By_Co
  untry_2001.xls
• To sort, click on a cell in the column you wish
  to sort by then click on the sort descending icon
  on the toolbar
• One would find that South Africa, India, and
  Nigeria have the highest number of adults with
  HIV.
• However, one cannot necessarily conclude that
  these countries have the worst problem with HIV
  since there are vastly different populations.

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Different Types of Relative Quantities

• Rate Rates are used to compare different types
  of variables
• Crimes per 1000 people
• Ratio Ratio are used to compare the same type of
  variable from two different sources
• Californias population is 33,872,000 and
  Oregons population is 3,431,000.
• Californias population is 33,872,000/3,431,000
  9.90 times larger than Oregons population.

• Tickets per person
• Miles per hour

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• Fraction or Percent Fractions or percents are
  used when comparing part to whole of the same
  type of variable
• Percent of adults with AIDS/HIV

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• Absolute change describes the actual increase or
  decrease from a reference (old) value to a later
  (new) value
• We use relative change to compare the absolute
  change to the reference (old) value

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Percentage Notation

• For communication purposes, we convert relative
  change (a fraction or decimal number) to a
  percentage (percentage change) generally with 2
  decimal places
• Three ways to convert decimals to percentage
• Move the decimal 2 places to the right
• Multiply by 100
• Use the button in Excel toolbar

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Example 1

• During a 6-month period Nokias stock doubled in
  price from 10 to 20.
• Calculate the absolute, relative and percentage
  changes in the stock price.
• Absolute change 20 - 10 10
• Relative change 10/10 1.0
• Percentage change 1.0 x 100 100

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• When a quantity Q doubles, what is its relative
  change? percentage change?
• Relative change (2Q Q)/Q Q/Q 1.0
• Percent change 1.0 x 100 100
• Will you get the same answer if the stock started
  at 5 and doubled to 10? If a service fee
  doubled from 25 to 50?
• YES

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Example 2

• The number of DVD players in homes in the United
  States increased dramatically from 1999 to 2001,
  from 5.4 million to 25.1 million. By how many
  percent did it rise from 1999 to 2001?
• .
• .

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Percentage Of

• The Formula (where the is written as a
  decimal)
• Visually Whole means the entire pie. Part means
  one of the shaded regions or pieces of the pie.

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• There are three ways to think about this
  relationship

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Solving Problems

• There are two approaches to solving the following
  problems.
• The first approach is to identify the two given
  numbers. Then you must decide which version of
  the part/whole relationship will help you answer
  the question.

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• The second approach is to remember the first
  formula, , fill in the information you are
  given and then solve for the missing variable.
• For all problems, remember to use the decimal
  version of the .

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Examples

• 2 is what percentage of 10?
• 2/10 .2
• 2 is 20 of 10
• 20 of what number is 2?
• Whole 2/.2 10
• 20 of 10 is 2
• What is 20 of 10?
• Part .210 2
• 20 of 10 is 2

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More Examples

• 17 is 32 of what number?
• whole 17/.32 53.125
• 17 is 32 of 53.125
• 67.2 is what percentage of 150?
• 67.2/150 .448
• 67.2 is 44.8 of 150

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• What is 233 of 71?
• Part 2.3371 165.43
• 165.43 is 233 of 71
• What is .7 of 50?
• Part .00750 .35
• .35 is .7 of 50
• 35 is 9 of what number?
• Whole 35/.09 388.89
• 35 is 9 of 388.89

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• 10,003 is what percentage of 1,762,325?
• 10,003/1,762,325 .00568
• 10,003 is .57 of 1,762,325
• one million three hundred thousand is what
  percentage of one billion?
• 1,300,000/1,000,000,000 13/10,000 .0013
• 1,300,000 is .13 of 1,000,000,000
• one thousand is what percentage of two thousand
  three hundred and six?
• 1,000/2,306 .4337
• 1,000 is 43.37 of 2,306

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Example 3

• In 2001, there were 654 drive-in theaters in the
  US, 77 fewer than in 1985. Approximately how
  many drive-in theaters were there in 1985?
• Whole 654/.77 849.35
• There were approximately 850 drive-in theaters in
  1985.

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Example 4

• DePauls undergraduate student body is
  approximately 21,000 students. 54 of the student
  body is female. Approximate how many females
  attend DePaul?
• Part .5421,000 11,340
• 11,340 females attend DePaul

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Example 5

• In Chicago in the year 2000, there were
  approximately 1.053 million African Americans,
  907 thousand whites (non-Hispanic), and 754
  thousand Hispanics, and 181 thousand others
  (other races or two or more races). What
  percentage of Chicagoans in 2000 were of Hispanic
  origin?
• 1,053 907 754 181 2895
• 754/2895 .2604
• 26.04 of Chicagoans were of Hispanic origin in
  2000

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Example 6

• The sales tax in Illinois is 8.75. The cashier
  rings up your purchase and tells you that your
  total bill is 103. What was the amount of your
  bill before taxes were added?
• 103 X .0875X X(1.0875) X1.0875
• X 103/1.0875 94.71
• (part whole/percent)

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Example 7

• You are in another state (not Illinois). You are
  buying a computer at Best Buy. The price before
  taxes is 949. When the cashier wrings up your
  purchase you owe 1005.94. What is the sales tax
  in this state? (You might be in Connecticut or
  Pennsylvania).
• 1005.94 949(1r)
• 1 r 1005.94/949 1.06
• r 1.06 1 .06 ? 6 sales tax

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The Mapping Tool

• Click on Map Tool at QRC Home Page
• http//qrc.depaul.edu/Excel_Files/HIV_Adults_By_Co
  untry_2001.xls
• Choose a map for your data
• Highlight only the cells with the geographic data
  you are mapping Copy and paste into tool
• Highlight only the cells with the numerical data
  you are mapping Copy and paste into tool
• Name your map and then make your shaded map