2.8.2: Exercise 2.8

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    MAKING CONNECTIONS TO THE COLLABORATION

    (1) Which of the following was one of the main mathematical ideas of the collaboration?

    (i) The Consumer Price Index (CPI) is an example of an index number that measures the cost of a basket of goods and services over time. It can be used to show inflation and deflation of prices.

    (ii) Inflation is calculated by finding the relative change in the CPI.

    (iii) The CPI is a ratio that compares the cost of goods to a base year in the form of a percentage. This is an example of how ratios are used for comparisons.

    (iv) The CPI always increases over time.

    DEVELOPING SKILLS AND UNDERSTANDING

    (2) The price of a first-class stamp has increased rapidly since the 1970s. The graph below shows the price (in cents) of a first-class stamp from 1917 to 2022.30

    Line graph showing the price (in cents) of a first-class stamp from 1914 to 2022. Y-axis represents the price (in cents), ranging from 0 to 60. X-axis represents the years, ranging from 1914 to 2014. Data line is shown starting in between 0 and 10 cents in 1914, remaining in between 0 and 10 cents until 1974, increasing steadily to finish just below 50 cents in 2014, and then to about 60 cents in 2022.

    (a) Estimate the absolute increase in the price of a first-class stamp from 2012 to 2022.

    (i) $0.05

    (ii) $0.15

    (iii) $0.25

    (v) $0.33

    (b) Estimate the relative increase in the price of a first-class stamp from 2006 to 2022.

    (i) 10%

    (ii) 25%

    (iii) 33%

    (iv) 50%

    (c) Suppose the absolute increase in the price of a first-class stamp from 2022 to 2032 is the same as it was from 2012 to 2022. What would the cost of a first-class stamp be in 2032?

    (i) $0.66

    (ii) $0.75

    (iii) $0.80

    (iv) $0.90

    (d) Suppose the relative increase in the price of a first-class stamp from 2022 to 2032 is the same as it was from 2012 to 2022. What would the cost of a first-class stamp be in 2032?

    (i) $0.60

    (ii) $0.66

    (iii) $0.80

    (iv) $0.90

    Urban Consumer Price Index (CPI-U)

    For Questions 3 and 4, refer to the CPI-U table in Collaboration 2.8. This table gives the cost of a representative basket of goods and services in base-year dollars (1983). The table shows the indices for selected years from 1913 to 2021. The Consumer Price Index (CPI-U) provides an indication of how the price of consumer goods changes over time.

    (3) In 2006, a 12-ounce coffee at Starbucks cost $1.46. In 2021, that same cup of coffee was $1.85.

    (a) What was the relative increase in the price of the cup of coffee from 2006 to 2021? Round to the nearest one percent.

    (b) What was the relative increase in the CPI-U from 2006 to 2021? Round to the nearest one percent.

    (c) Which of the following statements is true?

    (i) From 2006 to 2021, the price of coffee at Starbucks increased at a lower rate than the CPI-U.

    (ii) From 2006 to 2021, the price of coffee at Starbucks increased at the same rate as the CPI-U.

    (iii) From 2006 to 2021, the price of coffee at Starbucks increased at a higher rate than the CPI-U.

    (4) The rent on a building in 2008 was $1,350 per month. The landlord changes the rent relative to changes in the CPI-U. Use the CPI-U to calculate the rent in 2021. Round to the nearest dollar.

    (5) In Exercise 2.7, you examined productivity data for the G7 nations. The graph below shows another way of comparing productivity data using an index. Use the graph to answer the following questions. Note: These data are not the same as in the earlier problem.

    Vertical bar graph showing the comparison productivity data using an index. Y-axis represents the index (UK = 100), ranging from 80 to 140. X-axis represents the countries. Japan = in between 80 and 90 UK = N/A Canada = in between 100 and 110 Germany = in between 110 and 120 France = just over 100 Italy = in between 90 and 100 G7 excluding UK = at 100 US = about 140

    (a) How does Japan’s productivity compare to that of the United Kingdom?

    (i) Japan has a higher rate of productivity.

    (ii) Japan has a lower rate of productivity.

    (iii) Japan has about the same rate of productivity.

    (b) Which two countries have about the same rate of productivity?

    (c) Which country is used as the base?

    (d) What does the vertical scale represent?

    (i) Productivity in U.S. dollars

    (ii) Productivity in Euros

    (iii) Index numbers (percentages relative to a base)

    (iv) Population of each country

    (e) Which of the following statements are true?

    (i) The U.S. productivity is about $139.00 per worker.

    (ii) The U.S. productivity is about $39.00 per worker more than the U.K. productivity.

    (iii) The U.S. productivity is 39% higher than the U.K. productivity.

    (iv) The U.S. productivity is 139% higher than the U.K. productivity.

    (6) Data from the Census of Population and Housing surveys of 1974, ,1989, 2009, and 2021; the National Association of Realtors; and the U.S. Census Bureau are shown below.

     

    1974

    1989

    2009

    2021

    Median Family Income

    $13,020

    $34,400

    $60,600

    $70,780

    Median Price of House

    $86,751

    $84,622

    $185,000

    $346,900

    In which of these four years was a house most affordable?

    (i) 1974

    (ii) 1989

    (iii) 2009

    (iv) 2021

    MAKING CONNECTIONS ACROSS THE COURSE

    Now you will be expected to conduct Internet searches to find information. You will begin to encounter questions, such as the next one, that require you to identify the information you need and find the information from a reliable source.

    (7) According to Our World In Data, there were around 4,500,000 confirmed Covid-19 cases in Canada by the end of 2022. About 49,000 people in Canada had died of Covid-19 by the end of that year. In the United States, around 100,000,000 Americans were infected with Covid-19 by the end of 2022, and about 1,100,000 of those people died.

    (a) Use estimation to identify which of the following statements are true. There may be more than one correct answer.

    (i) There are more Covid-19 cases in Canada than in the United States.

    (ii) The Covid-19 infection rate was higher in Canada than in the United States.

    (iii) The death rate among people infected with Covid-19 is about the same in Canada as it is in the United States.

    (iv) By the end of 2022, the United States had about 20 times as many Covid-19 cases as Canada and about nine times the population.

    (b) Suppose that a new experimental drug being tested in Canada showed that it can decrease the death rate among people infected with Covid-19 by 18%. If this drug had been used by all Canadians infected with Covid-19, how many people would you have expected to die from Covid-19? Round to the nearest hundred people.

    (c) Suppose that the drug from (b) has the same influence on Americans infected with Covid-19. If the drug had been used by all Americans infected with Covid-19, how many people would you have expected to die from Covid-19? Round to the nearest thousand people.

    ________________________________________

    30 https://about.usps.com/who-we-are/postal-history/domestic-letter-rates-since-1863.htm

    This page titled 2.8.2: Exercise 2.8 was last modified on Wed, 15 May 2024 07:37:10 GMT and is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Carnegie Math Pathways (WestEd) .