1.6.2: Exercise 1.6

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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 number $14.6 trillion can also be written as $14,600 billion.

(ii) Credit cards are expensive to use if you do not pay off your balance each month. You pay more interest for cash advances than for the balance on purchases. Credit card debt is a problem in the United States.

(iii) A percentage is always a number greater than one.

(iv) Understanding numbers includes knowing how numbers compare in size, knowing what numbers represent in situations, and using estimation to answer questions about numbers.

DEVELOPING SKILLS AND UNDERSTANDING

(2) Below is the information from Question 5 in Collaboration 1.5, which you will use to answer (a) and (b) below.

Screen capture showing Brian's spreadsheet, indicating the following: A1 = Credit Card Charges for the Month A2 = Gas B2 = $56.08 A3 = Groceries B3 = $36.72 A4 = Restaurant B4 = $12.82 A5 = Movie tickets B5 = $16.00 A7 = Interest paid

Brian used the following expression to calculate his interest for that month’s charges.

= (0.2399 / 12) * (B2 + B3 + B4 + B5)

(a) A student used a different expression (shown below) to calculate Brian’s monthly interest. Choose the sentence that best explains what the expression means in terms of the context and the order in which the calculations were done. (Note: Spreadsheets use an asterisk (*) to indicate multiplication. For example, 3 * 4 means 3 × 4.)

= (0.2399 * B2 + 0.2399 * B3 + 0.2399 * B4 + 0.2399 * B5) / 12

(i) The student found the annual interest for each individual credit card charge, added to find the total annual interest, and then divided by 12 months to find the interest for 1 month.

(ii) The student distributed 0.2399 to the sum of the numbers and then divided by 12.

(iii) The student divided the annual interest rate by 12 to find the monthly interest rate, then multiplied each of the charges by that amount to find the monthly interest for each charge. The student then added the monthly interest for each charge together to find the total monthly interest.

(iv) The student multiplied each entry in the B column by 0.2399, added the results, and divided by 12 to find the final answer.

(b) Open a spreadsheet program like Excel or create a spreadsheet in Google Drive. Enter the information shown above into a new spreadsheet. Enter the formula given above:

= (0.2399 / 12) * (B2 + B3 + B4 + B5)

into cell B7. To do this, click on the cell. First type the equals sign (=). Note that a formula in a spreadsheet always starts with “=”. Type the formula. Notice as you type, your formula appears in the cell and also in the formula bar above the spreadsheet cells. Press enter and record the result (what appears in the cell) when you are done.

(3) Below is information from Question 1 in Collaboration 1.5, which you will use to answer (a) and (b) below.

“American household debt hit a record $14.6 trillion in the spring of 2021, according to the Federal Reserve.”

(a) Write the debt in standard form (written as a number like 374,000).

(b) What is the projected debt in scientific notation?

(i) 1.46 × 10¹²

(ii) 14,600 × 10¹²

(iii) 1.46 × 10¹³

(iv) 14.6 × 10¹²

(4) The Consumer Financial Protection Bureau has useful consumer information about credit cards. Go to the website www.consumerfinance.gov/credit-cards/knowbeforeyouowe. This is an interactive site in which you can get information by clicking on parts of the offer form. Use the information to answer the following questions.

(a) Which of the following can trigger a penalty annual percentage rate (APR)?

(i) You are late in paying your bill.

(ii) You pay your bill too early.

(iii) You do not use the credit card for six consecutive months.

(iv) You use your credit card every day.

(b) How can you avoid paying interest on purchases?

(i) Always make the minimum payment on time.

(ii) Avoid late fees.

(iii) Pay the entire balance by the due date.

(iv) Pay the minimum interest charge.

(5) A college student is talking to her family about a news story she read at InsideHigherEd.com.¹¹ It states:

Faculty members and students at Connecticut community colleges are concerned about a recent vote by the state Board of Regents to raise tuition at the institutions by 5 percent.

The student attends Gateway Community College in New Haven, Connecticut and paid about $4,700 in tuition in 2021. Which of the following statements is a good quantitative description of how her tuition will change for 2022 based on the news story? There may be more than one correct answer.

(i) Her tuition is going to increase by almost a half.

(ii) Her tuition will go up by more than $200.

(iii) Her tuition is going to double!

(iv) Her tuition will be around $5,000.

MAKING CONNECTIONS ACROSS THE COURSE

Big budget movies are tracked by investors and consumers. The following table gives data on the eight movies with the largest budgets that had been released as of August 22, 2022.¹² The data includes an estimate of the U.S. gross earnings and gross earnings in other countries. Gross earnings is the amount of money that a movie takes in.

Release Date	Movie	Budget	U.S. Gross Earnings	Gross Earnings Outside U.S.
5/18/2011	Pirates of the Caribbean: On Stranger Tides	$379,000,000	$241,071,802	$804,642,000
4/22/2015	Avengers: Age of Ultron	$365,000,000	$459,005,868	$943,803,672
4/24/2019	Avengers: Endgame	$356,000,000	$858,373,000	$1,939,128,328
4/25/2018	Avengers: Infinity War	$325,000,000	$678,815,482	$1,369,544,272
5/25/2007	Pirates of the Caribbean: At World’s End	$300,000,000	$309,420,425	$651,576,067
10/17/2017	Justice League	$300,000,000	$229,024,295	$428,902,692
5/23/2018	Solo: A Star Wars Story	$275,000,000	$213,767,512	$179,157,295
12/18/2019	Star Wars: The Rise of Skywalker	$275,000,000	$515,202,542	$558,946,737

(6) Write the number in words for the gross earnings outside the United States for Justice League.

(7) Which of the following calculations shows a correct method to estimate the net earnings for Pirates of the Caribbean: At World’s End? Net earnings is the total amount the movie makes after expenses (the budget) are taken out. There may be more than one correct answer.

(i) ($310,000,000 + $650,000,000) – $300,000,000 = $660,000,000

(ii) $650,000,000 – ($310,000,000 + $300,000,000) = $40,000,000

(iii) The budget and the U.S. gross earnings are about the same and cancel each other out. The net earnings would be about the same as the gross earnings outside the United States, or about 650 million dollars.

(iv) The gross earnings are about $650 million plus $300 million, or $950 million. The expenses are about $300 million. So, the net earnings are about 650 million dollars.

(8) Refer to the data for Star Wars: The Rise of Skywalker.

(a) Estimate the net earnings.

(b) Write a numerical statement to explain a way to estimate the net earnings using the budget and total gross earnings for Star Wars: The Rise of Skywalker, as in Question 7(i). This should look like the following, which was calculated for Pirates of the Caribbean: At World’s End: $960,000,000 - $300,000,000 = $660,000,000. Note that this example rounds figures to the nearest ten million so we can estimate easier. Use figures rounded to the nearest hundred million.

(9) The return on investment is the net earnings as a percentage of the budget. Which of the following statements best estimates the return on investment for Star Wars: The Rise of Skywalker? There may be more than one correct answer.

(i) The net earnings for Star Wars: The Rise of Skywalker were almost triple the investment.

(ii) The net earnings for Star Wars: The Rise of Skywalker were more than triple the investment.

(iii) The return on investment for Star Wars: The Rise of Skywalker was more than 300%.

(iv) The return on investment for Star Wars: The Rise of Skywalker was more than 200%.

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¹¹ https://www.insidehighered.com/news/2022/03/25/several-community-colleges-raise-tuition-fall

¹²http://en.Wikipedia.org/w/index.php?title=List_of_most_expensive_films, http://www.imdb.com/ ,and http://boxofficemojo.com/

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