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Mathematical Literacy 2
                         Module 4


                                   Answers to Case Studies



...
Case Study: MXit
What is MXit?
MXit is a mobile phone application used by over 4
 million youths across South Africa every...
Why is it so popular?
The mobile youth of today are constantly seeking
 new and innovative means to be in contact with
 ea...
Currently during peak time, and SMS on any one
 of our network providers costs around 80c for
 160 characters. Using MXit,...
1.Organise the profile of all the Mxit users into a
  table.

                                   Age                      ...
1. How many users are joining MXit every
   month?

       New users per month = new users per day x 30
       = 210 000 –...
1. What is the percentage increase per month of
   the MXit users?
    No of new users per month = 210 000 –360 000
    No...
1. What is the mean of the users that join every
   day?

          Mean value = (7000 + 12 000) / 2 = 9 500 users




Ans...
1. Draw a pie chart to illustrate the profile of users
   by age.
                                       Mxit users by age...
1. Draw a line graph per month for a period of one
   year to illustrate the growth of Mxit users.

                      ...
8.Interpret both the pie chart and the line graph.
  What do these two graphs reveal?

          The pie chart tells us th...
Case Study: iTunes
iTunes is a digital media player application, introduced by
Apple on January 10, 2001 at the Macworld E...
Case study: iTunes
•      History of songs sold on the Internet

•      September 12, 2006. Steve Jobs(CEO of Apple) repor...
Case study: iTunes
•      July 12, 2004. 100 million songs sold - mostly in the US, the three additional stores
       had...
Case study: iTunes
1. Compile a table of “tunes” sold over the period
   May 2003 – September 2006
       Date            ...
Case Study: iTunes
1. Draw a broken line graph with the dates
   (months) as x-values and the number of songs
   sold as y...
Answers to case studies module 4   Future Managers   17
Case Study: iTunes
1. From the graph determine how many tunes
   were downloaded in:
     –     August 2004
     –     Feb...
Answers to case studies module 4   Future Managers   19
Case Study: iTunes
1. From the graph determine how many tunes
   were downloaded in:
     –     August 2004               ...
Case Study: iTunes
1. If this growth in downloading of tunes
   continues, estimate how many tunes would
   have been sold...
Answers to case studies module 4   Future Managers   22
Case Study: iTunes
1. If this growth in downloading of tunes
   continues, estimate how many tunes would
   have been sold...
Case Study: iTunes
5. How many could be sold in January 2008




Answers to case studies module 4   Future Managers   24
Answers to case studies module 4   Future Managers   25
Case Study: iTunes
1. How many could be sold in January 2008
   Approx 3.5 billion songs




Answers to case studies modul...
Case Study: iTunes
1. Analyse the number of tunes sold by
   calculating:
     – Percentage increase between each year.
  ...
Case Study: iTunes
• Describe the growth of sales on the internet
   Sales are growing at an almost exponential rate i.e. ...
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NCV 2 Mathematical Literacy Hands-On Training Case Studies Module 4

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Solutions to Case Studies from Module 4 NCV 2 Mathematical Literacy Hands-On Training published by Future Managers (www.futuremanagers.net)

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NCV 2 Mathematical Literacy Hands-On Training Case Studies Module 4

  1. 1. Mathematical Literacy 2 Module 4 Answers to Case Studies Answers to case studies module 4 Future Managers 1
  2. 2. Case Study: MXit What is MXit? MXit is a mobile phone application used by over 4 million youths across South Africa every single day. This number increases by an astounding 7000-12000 new users per day. To explain in simple terms: It is a text chat application on a mobile phone. Answers to case studies module 4 Future Managers 2
  3. 3. Why is it so popular? The mobile youth of today are constantly seeking new and innovative means to be in contact with each other and to share information within their social networks. MXit offers and almost free chat application which enables users to have text chats with each other via mobile phone. The application is free and the only running costs are data charges from Cellular Networks, averaging to under 2 cents a message. Undercutting the costs of SMS services, MXit has spread like wildfire, 100 million messages are being sent within the community every day Answers to case studies module 4 Future Managers 3
  4. 4. Currently during peak time, and SMS on any one of our network providers costs around 80c for 160 characters. Using MXit, the exact same message will equate to around 3 to 5c! Profile of the Users: • By Sex: Female 45%; Male 55% • By Age: 0-11 (2.5%); 12 – 18 (42%); 19-25 (36%); 26+ (19.5%) Answers to case studies module 4 Future Managers 4
  5. 5. 1.Organise the profile of all the Mxit users into a table. Age % of Users 0-11 2.5% 12-18 42% 19-25 36% 26+ 19.5% Answers to case studies module 4 Future Managers 5
  6. 6. 1. How many users are joining MXit every month? New users per month = new users per day x 30 = 210 000 – 360 000 new users per month 5. What is the rand value of all messages sent on a day? Rand Value = no of messages x cost of message = 100 million x 3 cents = R3 million Answers to case studies module 4 Future Managers 6
  7. 7. 1. What is the percentage increase per month of the MXit users? No of new users per month = 210 000 –360 000 No of total users = 4 000 000 % Increase per month = 210000 / 4000000 x 100 = 5.25% (min) % Increase per month = 360 000 / 4000000 x 100 =9% (max) Answers to case studies module 4 Future Managers 7
  8. 8. 1. What is the mean of the users that join every day? Mean value = (7000 + 12 000) / 2 = 9 500 users Answers to case studies module 4 Future Managers 8
  9. 9. 1. Draw a pie chart to illustrate the profile of users by age. Mxit users by age 0-11 26+ 3% 20% 12-18 41% 19-25 36% Answers to case studies module 4 Future Managers 9
  10. 10. 1. Draw a line graph per month for a period of one year to illustrate the growth of Mxit users. Growth of Mxit users in one year 8000000 7000000 6000000 5000000 4000000 3000000 2000000 1000000 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Answers to case studies module 4 Future Managers 10
  11. 11. 8.Interpret both the pie chart and the line graph. What do these two graphs reveal? The pie chart tells us that the largest user group of Mxit users is teenagers (12-18), while users from 19-25 still represent a significant portion. The line graph tells us that the number of Mxit users is growing at a constant (linear) rate. This gives us some power to predict the number of users in the future. Answers to case studies module 4 Future Managers 11
  12. 12. Case Study: iTunes iTunes is a digital media player application, introduced by Apple on January 10, 2001 at the Macworld Expo in San Francisco, for playing and organizing digital music and video files on your computer. The program is also an interface to manage the contents on Apple’s popular iPod digital media players as well as the recently introduced iPhone. Additionally, iTunes can connect to the iTunes Store (provided an internet connection is present) in order to download purchased digital music, music videos, television shows and iPod games. Answers to case studies module 4 Future Managers 12
  13. 13. Case study: iTunes • History of songs sold on the Internet • September 12, 2006. Steve Jobs(CEO of Apple) reports 1.5 billion songs sold. • February 23, 2006. 1 billion songs sold. One notable addition to the list of countries at this point was Japan, and there were a number of sub-sites, like a French and a Dutch site for Belgium. • July 17, 2005. 500 million songs sold. At this point, iTunes was available in 19 countries: US, Austria, Belgium, Canada (excluding the Province of Quebec), Denmark, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, Netherlands, Norway, Portugal, Spain, Sweden, Switzerland, and the UK. • May 10, 2005. 400 million songs sold. iTunes opens in Denmark, Norway, Sweden and Switzerland • January 24, 2005. 250 million songs sold. Answers to case studies module 4 Future Managers 13
  14. 14. Case study: iTunes • July 12, 2004. 100 million songs sold - mostly in the US, the three additional stores had only opened less than a month earlier. • June 15, 2004. iTunes opens in the UK, France, and Germany. • April 28, 2004. 70 million songs sold. • March 15, 2004. 50 million songs sold. • December 15, 2003. 25 million songs sold. • October 16, 2003. iTunes available for Windows. 13 million songs sold. • September 8, 2003. 10 million songs sold. • June 23, 2003. 5 million songs sold. • May 14, 2003. 2 million songs sold. • May 5, 2003. One million songs sold. Managers Answers to case studies module 4 Future 14
  15. 15. Case study: iTunes 1. Compile a table of “tunes” sold over the period May 2003 – September 2006 Date Songs sold May, 5 2003 1 million May 14, 2003 2 million June 23, 2003 5 million September 8, 2003 10 million October 16, 2003 13 million December 15, 2003 25 million March 15, 2004 50 million April 28, 2004 70 million July 12, 2004 100 million October 14, 2004 150 million December 16, 2004 200 million January 24, 2005 250 million May 10, 2005 400 million July 17, 2005 500 million February 23, 2006 1 billion September 12, 2006 1.5 billion Answers to case studies module 4 Future Managers 15
  16. 16. Case Study: iTunes 1. Draw a broken line graph with the dates (months) as x-values and the number of songs sold as y-values. Use the following scale: 50 million = 1cm and 1 month = 1cm Answers to case studies module 4 Future Managers 16
  17. 17. Answers to case studies module 4 Future Managers 17
  18. 18. Case Study: iTunes 1. From the graph determine how many tunes were downloaded in: – August 2004 – February 2005 – October 2005 – April 2006 – July 2006 Answers to case studies module 4 Future Managers 18
  19. 19. Answers to case studies module 4 Future Managers 19
  20. 20. Case Study: iTunes 1. From the graph determine how many tunes were downloaded in: – August 2004 120 million – February 2005 280 million – October 2005 680 million – April 2006 1100 million – July 2006 1320 million Answers to case studies module 4 Future Managers 20
  21. 21. Case Study: iTunes 1. If this growth in downloading of tunes continues, estimate how many tunes would have been sold in January 2007 Answers to case studies module 4 Future Managers 21
  22. 22. Answers to case studies module 4 Future Managers 22
  23. 23. Case Study: iTunes 1. If this growth in downloading of tunes continues, estimate how many tunes would have been sold in January 2007 Approximately 1.7 billion songs Answers to case studies module 4 Future Managers 23
  24. 24. Case Study: iTunes 5. How many could be sold in January 2008 Answers to case studies module 4 Future Managers 24
  25. 25. Answers to case studies module 4 Future Managers 25
  26. 26. Case Study: iTunes 1. How many could be sold in January 2008 Approx 3.5 billion songs Answers to case studies module 4 Future Managers 26
  27. 27. Case Study: iTunes 1. Analyse the number of tunes sold by calculating: – Percentage increase between each year. – What is the Mean, Mode and Median years between October 2004 – September 2006? Year Number of iTunes % increase sold Oct 2004 120 million ---------------- Oct 2005 620 million 416% Sept 2006 1480 million 138% Answers to case studies module 4 Future Managers 27
  28. 28. Case Study: iTunes • Describe the growth of sales on the internet Sales are growing at an almost exponential rate i.e. the graph is getting steeper. As the market saturates we may expect to see the graph become more linear over time (closer to a straight line). This is because no new customers will be taken on board, but the current ones will continue to order. Answers to case studies module 4 Future Managers 28

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