MATH 1030 Walden University W

Discussion: Inequality in Our World 

Inequalities are present in our everyday lives. You may budget to spend less than $100 on groceries or plan to spend more than 2 hours a week exercising. Both of these statements involve budgeting resources, such as time and money. However, unlike last week where only one value could solve our T=15h equation, these statements allow for a variety of situations that meet the requirements for a solution. For example, in looking at the grocery situation, a bill of $90, $85, or $98 would all fit the criteria of spending less than $100. 

To break this down further, you might assume that a grocery bill of $90 would include items purchased from different departments of the grocery store. Meats, vegetables, dairy, and paper products might be subgroups represented by the overall group—groceries. The value of each subgroup would not be equally represented in your grocery bill. 

What other situations can you imagine where the variables, or subgroups, do not equally represent the whole group?

In this Discussion, you examine the groups and subgroups that may exist in your field of study or current workplace. You also explore how to diagram these groups using abstract math. 

To prepare for this Discussion:

  • Review the TED Talk on abstract math, paying particular attention to how Eugenia Cheng (2018) explains how pure mathematics models social inequality.
  • Think about an overall group that may exist in your environment.
  • Identify three subgroups within the overall group, and diagram these groups as Cheng (2018) did in the presentation using the following format where a/b/c are your individual subgroups:
    • {a,b,c}
    • {a,b}, {a,c}, {b,c}
    • {a}, {b}, {c}
    • { }
  • Think about two inequality statements that can be inferred from the diagram referring to the specific groups that you have just created. For example, if a represents dogs and c represents cats then and inequality could be: dogs>cats.
  • Using the problem-solving techniques from Week 1, decide if these inequalities are true based on the overall group you selected.
  • Consider one potential bias or inequality that may exist in either Level 2 or Level 3 of your diagram and think about how it would create an unequal ranking between the elements on this level.
  • Think about what the inequality would be in the context of your situation and think about how it would be expressed as a mathematical inequality.
  • Consider who might be interested in these results, and why.

Post at least 2 paragraphs responding to the following prompts: 

  • Provide diagram created based on your example of social inequality.
  • Write one inequality statements that can be inferred from your diagram, referring to your specific sub-groups (not the variables a/b/c).
  • Explain whether you feel these inequalities are true.
  • Express your conclusion as a mathematical inequality.
  • Explain who might be interested in these results, and why.

MATH 1030 Walden University W

Week 5: Consumer Mathematics

Everyone benefits from effective money management. Money is earned, bills are paid, and savings accounts are created. But what happens when the money you earn is not enough to cover your immediate needs or wants? This is where a loan comes in.

No matter how much money you make in your lifetime, it is likely that at some point you will take out a loan. This could be for education, a home, a car, or a hobby, such as a boat. If you have taken out a loan, you already know there is a cost for taking that loan. How much of that loan is interest, or money paid to the financial institution for lending you the cash? How much of your monthly payment is paying down the debt, and how much is paying interest on that amount? If you haven’t taken out a loan before, you will be glad to work through this math now so that you are prepared for the true costs involved.

This week, you will explore the math behind finances, loans, and interest payments. You also re-examine your own personal financial management techniques.

Discussion: Repaying Loans

Before taking out a loan, it is important to know the repayment terms and how your interest rate and the time of the loan affect the total loan balance.

For this Discussion, you examine the effect of simple and compound interest, as well as time on the principal balance of a loan. You also explore how these variables affect loan repayment.

To prepare for this Discussion:

  • Think of a big-ticket item you might need to take out a loan to purchase. Dream big. What have you always wanted? This could be a boat, car, motorcycle, a trip around the world, etc. Research the cost of this item.
  • Select a reasonable interest rate for your item (between 2% and 10% is standard).
  • Select a time period to pay off your loan (between 3 and 10 years is common
  • Post at least 2 paragraphs in response to the following:
    • Paragraph 1:
      • Describe the item you are taking a loan out for and the purchase price.
      • Include your chosen interest rate and amount of time for your loan.
      • Determine the amount of interest you will pay throughout the term of the loan and the final cost of the item when the loan is paid in full. Note: Assume your bank uses the simple interest formula: Interest = Principal * Rate * Time.
      • Show the work needed to find the amount of interest and total cost.
      • Determine the monthly payment for this loan.
    • Paragraph 2:
      • Repeat the interest computation however lower the time frame by one year. Show your work.
      • Determine the total amount of the loan when paid in full.
      • Compute the new monthly payment.
      • Explain if you are surprised by the results. Why, or why not?
      • Discuss one change you could make in your life to make the new monthly payment possible.

MATH 1030 Walden University W

Response 1: Respond to at least one classmate using the following:

  • Review the type of technology your classmate chose to focus on.
  • What phase of technology do you believe this particular piece of technology was in during the year 2000?
  • What phase do you believe it is in now? Justify your reasoning.

Classmate that will respond to for the first response will be:

Sabrina,

Week 3: Changing Technology

For this week’s discussion I chose the graph that depicts the cost per minute for long-distance calls to India that Anderson (2004) used as an example for the last stage of any viable technology, approaching free. The values on the Y-axis represent the cost per minute and the X-axis represents years. Starting in 1990, the cost per minute was around $2.25 and the graph shows a slow change at first although long-distance calls were commoditized. As the technology advanced with the over-abundance of fiber-optics, costs began to drop as low as .50 cents per minute in the year 2000. According to the graph, we can see that the cost for long-distance calls were close to approaching free as the line descends which means that there is a negative slope.

The y-intercept isn’t present on the graph, but I would estimate that it would be around $2.25 seeing that for the first 3 years the cost per minute was virtually the same.

To calculate the slope (m) between the points (1995, 1.5) and (2000, 0.5) I need to compare the change in y to the change in x (Blitzer, 2019).

m = y2-y1/x2-x1

m= (0.5 – 1.5) / (2000 – 1995) = -1/5

Since the slope is negative, this means that as time progress the cost of long-distance call decreases as the line descends from left to right.

If we use this graph to predict the cost of long-distance calls to India, by the year 2025 that cost would be basically non-existent. While it would be nice to see all phone plans include international calls at no extra cost, I do not believe that this prediction is reasonable because I don’t see carrier services and VoIP companies letting go of their profits so easily. I am just glad to see that international calls are not as costly as in the past so that we can easily connect with our loved ones throughout the world.

References:

Anderson, C. (2007, April 27). Technology’s long tail [Video]. TED Talks. https://www.ted.com/talks/chris_anderson_technolog…

Blitzer, R. (2019). Thinking mathematically (7th ed.). Pearson.

Response 2: Respond to at least one other classmate using the following:

  • Review the graph your peer chose. Do you feel it is reasonable to use the pattern on the graph to predict the Y value for the year 2025? Why or why not?

the second classmate response you will be responding to:

Maria,

We have experienced many changes with the coronavirus pandemic, but these changes has also been reflected in the global retail industry. Individuals stayed at home and shopped using their smart phone and home computers than making purchases in-store. According to Statista, the top three retail websites worldwide in 2020 were Amazon.com, e-Bay.com, Rakuten.co.ip, Apple.com and Samsung.com (Coppola, 2021. Statista). Although individuals are transitioning back to the office for work, digital buyers continue to grow, worldwide.

“In June 2020, global retail e-commerce traffic stood at a record 22 billion monthly visits, with demand being exceptionally high for everyday items such as groceries, clothing, but also retail tech items” (Coppola, 2021. Statistista). The Digital buyers in billions is represented by the y-axis. The x-axis would represent the years, 2014 through 2021. The two variables are y = Digital buyers in billions and x = Year 2014-2021. Given the current slope the anticipated digital buyers in 2025 would be 2.62 based on the slope of .82/7 = 0.117 = 0.12

y=mx + y=.12x + 1.2

Slope = Change in y y = mx + b

Change in x

y x

1.32 1 (2014)

1.46 2 (2015)

1.52 3 (2016)

1.66 4 (2017)

1.79 5 (2018)

1.92 6 (2019)

2.05 7 (2020)

2.14 8 (2021)

2.62 12 (2025)

Statista. (Coppola, 2021)

https://www.statista.com/topics/871/online-shoppin…

MATH 1030 Walden University W

Week 3: Graphing Equations—Linear Functions and Systems of Equations

Graphs are often used to visualize the relationship between two variables. You will find graphs in media, academic, and professional life. Relationships, such as those between wind speed and temperature, supply and demand, or sales and time of year, can be difficult to interpret if looking at tables of numbers. A graph can clearly show that sales of winter coats dip in June while ice cream sales rise.

    For example, when comparing two cell phone companies you might find:

    • Company 1 charges $40 a month plus $15 per gigabyte (g) of data. The plan’s total cost can be modeled as follows:

      C= 40+15g

      Where C is Company 1, 40 is the monthly cost, and 15g is the surplus charge of $15 for each additional gigabyte of data.

    • Company 2 charges $60 a month plus $10 per gigabyte of data. This plan can be modeled with the following equation:

      C=60+10g

    Photo Credit: Note. This graph is for educational purposes only.

Both equations can be graphed to visualize the total charges of each company based on how many gigabytes of data you anticipate using. When determining which company’s offering is the best choice for you, it might be useful to determine at what point the cost of the two companies is equal. Solving systems of equations will reveal this solution.

This week, you will examine how to plot points in a rectangular coordinate system and graph equations and functions. You will also explore how to solve application problems using systems of equations.

Discussion: Changing Technology

Technology changes every minute of every day. Not being able to access the web instantly seems almost impossible for the next generation to fathom. Most children born today will never know the sound of a dial-up modem. Changes in technology can be measured using the basic premise of slope or rate of change to examine patterns. Chris Anderson explores the life of technology in a dated 2004 TED Talk. Be aware the data is old (and you may get a chuckle out of some of it), however, the concept of measuring the life of technology is not.

For this Discussion, you examine the components and patterns of a graph and explore interpretations that can be derived from the placement of variables on a graph.

To prepare for this Discussion:

  • Review the video on technology’s long tail and select one of the graphs presented in the video.
  • Reflect on what the graph you selected shows, including what variables are on the x- and y-axis and what patterns are displayed on the graph. Be sure to consider all the key points as presented on the graph.
  • Think about two points on the graph you selected. Consider how you would write these points, as ordered pairs, and determine the slope between the two points. It is recommended that you pause the video to make it easier to identify two points.
  • Approximate the y-intercept of the graph you selected. If the y-intercept is not visible on your graph, select a reasonable value for it, and think about why you chose it.
  • Think about how you would write an equation for the line in the form of y=mx+b using the y-intercept (b) and slope (m), and how you would interpret the slope as a rate of change, including what it means in terms of change for both variables.
  • Consider a prediction you might make for the year 2025 on your graph, using the slope value as a rate of change, and think about whether or not you feel the prediction is reasonable. Why

below is the video and transcript that need to be referenced and cited:

1. Anderson, C. (2004, February). Technology’s long tail [Video]. TED Conferences. https://www.ted.com/talks/chris_anderson_technology_s_long_tail
Note: The approximate length of this media piece is 14 minutes.

Technology’s Long Tail Transcrip

2. https://www.youtube.com/watch?v=Cddn2OlcflA&t=4s

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