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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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Mathematical Literacy 2Module 4
Answers to Case Studies
Answers to case studies module 4 1Future Managers
Case Study: MXitWhat 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 2Future Managers
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 3Future Managers
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 4Future Managers
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 5Future Managers
2. How many users are joining MXit every month?
3. What is the rand value of all messages sent on a day?
New users per month = new users per day x 30
= 210 000 – 360 000 new users per month
Rand Value = no of messages x cost of message
= 100 million x 3 cents
= R3 millionAnswers to case studies module 4 6Future Managers
4. 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 7Future Managers
5. 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 8Future Managers
6. Draw a pie chart to illustrate the profile of users by age.
Mxit users by age
0-113%
12-1841%
19-2536%
26+20%
Answers to case studies module 4 9Future Managers
7. 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
0
1000000
2000000
3000000
4000000
5000000
6000000
7000000
8000000
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Answers to case studies module 4 10Future Managers
8.Interpret both the pie chart and the line graph. What do these two graphs reveal?
Answers to case studies module 4 11Future Managers
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.
Case Study: iTunesiTunes 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 12Future Managers
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.
• December 16, 2004. 200 million songs sold.
• October 14, 2004. 150 million songs sold. Answers to case studies module 4 Future Managers 13
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.
• April 28, 2003. iTunes launched in United States. Answers to case studies module 4 Future Managers 14
Case study: iTunes1. Compile a table of “tunes” sold over the period
May 2003 – September 2006
Answers to case studies module 4 Future Managers 15
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
Case Study: iTunes2. 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
Answers to case studies module 4 Future Managers 17
Case Study: iTunes3. 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
Answers to case studies module 4 Future Managers 19
Case Study: iTunes3. 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
Case Study: iTunes4. 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
Answers to case studies module 4 Future Managers 22
Case Study: iTunes4. 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
Case Study: iTunes5. 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: iTunes5. How many could be sold in January 2008
Approx 3.5 billion songs
Answers to case studies module 4 Future Managers 26
Case Study: iTunes6. 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?
Answers to case studies module 4 Future Managers 27
Year Number of iTunes sold
% increase
Oct 2004 120 million ----------------
Oct 2005 620 million 416%
Sept 2006 1480 million 138%
Case Study: iTunes• Describe the growth of sales on the internet
Answers to case studies module 4 Future Managers 28
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.