Topics: Functions, Linear functions
An International Comparison of Cell Phone Plans and Prices ANSWER KEY
http://newamerica.net/publications/policy/an_international_comparison_of_cell_phone_plans_an
d_prices
The study was completed by New America Foundation’s Open Technology Initiative (OTI) on
the costs and types of cell phone packages available to consumers around the world. The results
of the study provide some insight into business models in several key countries. For example, in
some countries, contract plans (postpaid) are more prevalent than prepaid plans (pay-as-you go
phones). The comparison was done between prominent cell phone carriers in 11 countries.
Voice Service
Key Findings: Across postpaid and prepaid voice plans, Canada, U.S., U.K. and Japan mostly
fall in the high to middle price tiers while India, Hong Kong and Sweden fall in the low price
tier.
1) Let x be the number of minutes. Find monthly cost ($) as a function in terms of x (number of
minutes) for the postpaid plan in Denmark. What is the cost if 180 minutes are used in one
month? What is the domain of this function (hint: consider monthly limit on minutes)?
C(x) = 0.07x
Domain: [0, 240]
C(180) = $12.60
Julia Nudel, Valencia College (2014), College Algebra
2) Find monthly cost ($) as a function in terms of x (number of minutes) for the postpaid plan in
India. What is the cost if 180 minutes are used in one month?
C(x) = 0.01x
C(180) = $1.80
3) Find monthly cost ($) as a function in terms of x (number of minutes) for the postpaid plan in
U.K. What is the domain of this function? Can 180 minutes be used under this plan?
C(x) = 0.17x
Domain: [0, 100]
No, x = 180 is outside of the domain
4) According to this study, which 3 countries have the cheapest postpaid plan (consider $/min)?
Hong Kong, India, Sweden
5) Which 3 countries have most expensive plan?
Canada, U.K., U.S.
Text Service
Key Findings: U.S. is in the highest price tier in the postpaid and prepaid text plans sharing
space with U.K., Canada and Denmark while Sweden, India and Japan fall in the lowest price
tier.
Julia Nudel, Valencia College (2014), College Algebra
1) Calculate the cost per text in the postpaid plan in Sweden. How many times is the cost per text
in U.K. is more expensive than cost per text in Sweden?
Cost per text =
17.80
≈ $0.003 per min
5500
The cost in U.K. ($0.10 per text) is about 3.3 times higher than in Sweden.
2) Which countries have no preset monthly limits on texts?
Hong Kong, India, Japan, Sweden, South Korea
3) Which 2 countries have the cheapest unlimited plan (cost per text)? Which 2 countries have
most expensive unlimited plan?
India and Sweden have cheapest unlimited plans.
U.S. and Canada have most expensive unlimited plans.
Julia Nudel, Valencia College (2014), College Algebra
Minimum Cost of a Complete Cell Phone Package
To get a holistic picture of the cost of a cell phone service, it is necessary to look at the total cost
of all three services: voice, text and data. We will arrive at the final cost to the consumer by
looking at the sum of the minimum monthly cost of each of the best available postpaid voice,
text and data plans.
How does the overall package (including voice, text and data) in U.S. compare to other countries
in this study?
Sample answer: U.S. offers plans in more expensive to medium range in all 3 categories and
overall price per month.
Read the rest of the article (follow the link above). How does your conclusion compare to the
conclusion reached in the article?
Answers may vary.
Bonus: If Pay-as-you-go voice service plan in Canada costs 0.4 CAD per minute (Canadian
dollars) and in Denmark a similar service costs 0.99 DKK per minute (Danish krone). How many
times is the service in Canada more expensive than in Denmark? Hint: you may need to look up
current currency conversion rates for Canada and Denmark.
Julia Nudel, Valencia College (2014), College Algebra
Answers may vary depending on current currency conversion rate:
0.4 CAD ≈ $ 0.36 (cost per min)
0.99 DKK ≈ $0.17 (cost per min)
The service in Canada costs about twice as much as in Denmark.
If Pay-as-you-go voice service plan in Finland costs € 0.08 per min and in Hong Kong a similar
service costs 0.15 HKD per minute (Hong Kong dollars). How many times is the service in
Finland more expensive than in Hong Kong?
Answers may vary depending on current currency conversion rate:
€ 0.08 ≈ $ 0.11
0.15 HKD ≈ $0.02
The service in Finland is about 5 times as expensive as in Hong Kong.
Julia Nudel, Valencia College (2014), College Algebra