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

Mathematical Literacy 2
Module 4

Answers to Case Studies

Answers to case studies module 4 Future Managers 1

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.


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

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%)


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%


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

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)


1. What is the mean of the users that join every
day?

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


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%


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


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.

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.

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.

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

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

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


Case Study: iTunes
1. From the graph determine how many tunes
were downloaded in:
– August 2004
– February 2005
– October 2005
– April 2006
– July 2006


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


Case Study: iTunes
1. If this growth in downloading of tunes
continues, estimate how many tunes would
have been sold in January 2007


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


Case Study: iTunes
5. How many could be sold in January 2008


Case Study: iTunes
1. How many could be sold in January 2008
Approx 3.5 billion songs


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%


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.


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

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