2.5.2: Exercise 2.5

MAKING CONNECTIONS TO THE COLLABORATION

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

(i) To calculate a percentage, move the decimal in the percentage rate two places to the left and multiply times the reference value.

(ii) Smoking increases your chance of a heart attack.

(iii) Consider this situation: 20% of a population gets a certain illness. A vaccine can reduce the infection rate by 10%. Out of 100 people, the reference value for the 10% reduction would be the full population (or 100 people).

(iv) Consider this situation: 20% of a population gets a certain illness. A vaccine can reduce the infection rate by 10%. Out of 100 people, the reference value for the 10% reduction would be the 20 people who are projected to get the illness.

DEVELOPING SKILLS AND UNDERSTANDING

(2) Think back to your work from Question 2 and 3 in Collaboration 2.5 to answer the following questions.

(a) In class, you used a group with 500 people. Repeat the work with a group of 100 people.
Group 1 has a 40% risk of heart attack and Group 2 has a 10% risk. Complete the table.

(b) Select the true statement:

(i) The size of the group does not change anything about the results for the group.

(ii) The size of the group changes the number of people who are expected to have a heart attack with the drug, but it does not change the percentage.

(iii) The size of the group does not change the number of people who are expected to have a heart attack with the drug, but it does change the percentage.

(iv) The size of the group changes the number and the percentage of people who are expected to have a heart attack with the drug.

(3) The University of Washington is a large public university, while the University of Puget Sound is a small private university.

(a) If both of these universities are expecting 12% more freshmen next year, which university will see the greatest absolute change in the number of freshmen? (Choose the best answer.)

(i) Since the University of Washington is larger, they have more freshmen to begin with. Thus, a 12% increase will not translate to a larger absolute change.

(ii) Since the University of Washington is larger, they have more freshmen to begin with. Thus, a 12% increase will translate to a larger absolute change.

(iii) Both will undergo the exact same absolute change.

(iv) Since the University of Puget Sound is smaller, they have fewer freshmen to begin with. Thus, a 12% increase will translate to a larger absolute change.

(b) Which university will see the greatest relative change in the number of freshmen?

(i) University of Washington

(ii) University of Puget Sound

(iii) Both universities will undergo the same relative change.

(4) Suppose that the populations of the United States and China both undergo the same absolute change in one year. Which undergoes the larger relative change?

(i) The United States would undergo the smaller relative change, since the population of China is so much larger than that of the United States.

(ii) China would undergo the larger relative change since the population of the United States is much smaller than that of China.

(iii) The United States would undergo the larger relative change since the population of the United States is so much smaller than that of China.

(iv) The two countries would undergo the exact same relative change.

(5) Suppose that the populations of the United States and China both increase by 12 million people in one year. What would be the relative change for each country? Answer to the nearest tenth of a percent.

(a) If you assume that the U.S. population is about 333 million, an increase of 12 million would result in a relative change of ___________%.

(b) If you assume that China has about 1.4 billion people, an increase of 12 million would result in a relative change of ___________%.

(6) Employees at a certain company currently have to pay 3% of their health care costs, while the company pays the rest. Next year, however, employees will have to pay 6% of their health care costs. Express this change as an absolute change (in percentage points) and as a relative change.

(a) Absolute change: ____________ percentage points.

(b) Relative change: _____________%.

MAKING CONNECTIONS ACROSS THE COURSE

(7) The graph below is based on information from the 2020 U.S. Census.¹⁷ Use the graph to answer the questions.

(a) Which is the best estimate of the total population for age group 0–9?

(i) 400

(ii) 40,000

(iii) 40,000,000

(iv) 400,000,000

(b) Which is the best estimate for the total population of age group 70–79?

(i) Two hundred and four

(ii) Two hundred and four thousand

(iii) Two hundred and four million

(iv) Twenty four million

(c) Which statement is the most accurate?

(i) There are fewer than 10,000,000 people age 70 and older.

(ii) There are between 10,000,000 and 20,000,000 people age 70 and older.

(iii) There are between 20,000,000 and 30,000,000 people age 70 and older.

(iv) There are between 30,000,000 and 40,000,000 people age 70 and older.

(d) An advertiser is considering two advertising campaigns for a product. Campaign A is most effective for ages 20–39, while Campaign B is most effective for ages 30–49. Which campaign should the advertiser choose to reach the most people?

(i) Campaign A

(ii) Campaign B

______________________________________________

¹⁷ https://www.census.gov/data/tables/time-series/demo/popest/2020s-national-detail.html