Math Problems with a Global Context #1
College Algebra (Acosta and Karwowski, 2012)
1. Quadratic Functions & Operational Functions:
Dubai is one of the seven United Arab Emirates
located in the Persian Gulf. As of January 2011, the
Burj Khalifa was the world’s tallest building, over
160 stories high and reaching 2,716.5 feet. Off the
coast of Dubai is “The World,” a cluster of 300
manmade islands along with the “Palm Trilogy,” an
island in the shape of a palm tree; both were
created from sand dredged from the sea. Sources:
www.burjkhalifa.ae; www.hotliermiddleeast.com;
www.dubaitourism.ae
A tennis team travels to Dubai and is having a
contest to see whose group can launch the highest
tennis ball from the 1,483 food observatory deck of
the Burj Khalifa, the world’s tallest building as of
January 2011. The height in feet of team A’s tennis
ball can be modeled by f(t) = - 16t2 = 73t = 1483 and
the height of team B’s tennis ball can be modeled
by g(t) = - 16t2 = 60t = 1483, where t represents
time in seconds.
a. Find (f + g)(t) and interpret its meaning.
b. Find (f + g)(5.5) and interpret its meaning.
c. Find (f - g)(t) and interpret its meaning.
d. Find (f - g)(2) and interpret its meaning.
e. The building has 163 floors. Use your regression line to extrapolate and predict its height in meters. Look up the actual height of this
building on the internet and see how close your prediction was.
Follow up Thought/Discussion Questions:
1. What factors might contribute to the fact that the tallest building in the world is located in the Middle East instead of another part of the
world?
2. The Clock Tower complex in Saudi Arabia is actually the largest hotel in the world with over 8000 rooms. Why might a hotel of this size be
needed in this location of the Middle East?
Kurt Overheiser, Julia Nudel, and Damion Hammock, Valencia College (2014), College Algebra
Math Problems with a Global Context #1
College Algebra (Acosta and Karwowski, 2012)
2. Logarithmic Functions:
Consider the following earthquakes: On January 12, 2010, Haiti suffered a
major earthquake of magnitude 7.0 that left an estimated 222,570 people
killed, 300,000 injured, 1.3 million displaced, 97,294 houses destroyed, and
188,383 houses damaged in Port-au-Prince area and in much of southern
Haiti.
On December 26, 2004, the ocean floor of Sumatra, Indonesia was the
epicenter of an earthquake of magnitude of 9.3. This earthquake also
caused a disastrous tsunami that washed away whole cities in Indonesia.
More than 240,000 people died from the quake and tsunami combined.
a. Find the intensity of the 2004 earthquake. Express its intensity in terms
of the intensity of a standard earthquake that is Io.
b. Find the intensity of the 2010 earthquake. Express its intensity in terms
of the intensity of a standard earthquake that is Io.
c. Compare the intensity of the 2004 earthquake with the one in 2010.
Sources: www.earthquake.usgs.gov; www.mapsofworld.com
3. Topic? In 1960, the world’s strongest earthquake was recorded in Chile with a magnitude of 9.5 on the Richter scale. The death toll is not
known, but it is estimated that it may have caused as much as $800 billion US Dollars in damage. Calculate the intensity of this earthquake
in terms of the intensity of a standard earthquake, Io, and compare this intensity with that of the 2004 Indonesia earthquake discussed
above. Source: www.earthquake.usgs
Kurt Overheiser, Julia Nudel, and Damion Hammock, Valencia College (2014), College Algebra
Math Problems with a Global Context #1
College Algebra (Acosta and Karwowski, 2012)
4. Exponential Decay: In 1991, “Otzi” the iceman was
discovered by Erika and Helmut Simon, a vacationing
German couple hiking on the Hauslabjoch Pass in Italy.
Carbon dating of samples from the site allowed scientists to
conclude that the iceman had died of hypothermia
approximately 5,300 years ago. Since the body was soon
covered by snow at the time of death, this virtually
eliminated damage from decomposition. The equation N =
Noe -0.000120942t gives the amount of carbon-14 in a sample,
where No represents the original amount of carbon-14 in
the living tissue, the t equals time in years. Since it has
been established that the iceman had died approximately
5,300 years prior to the discovery, use the given equation
to determine what percentage of the original carbon-14 in
his body was remaining in 1991.
Sources: www.nationalgeographic.com; www.pbs.org;
www.mummytombs.com
Kurt Overheiser, Julia Nudel, and Damion Hammock, Valencia College (2014), College Algebra
Math Problems with a Global Context #1
College Algebra (Acosta and Karwowski, 2012)
5. Exponential Functions: The country of Iceland is near the Arctic Circle,
and it consists of one large island and numerous smaller ones. The country
is referred to as “the land of ice and fire,” due to its numerous glaciers, fjord,
and over 200 volcanoes. Iceland’s Eyjafjallajökull volcano erupted on April
14, 2010, causing nearby evaluations and stranding millions of airline
passengers throughout Europe.
In 2003, the population of Iceland was approximately 290,570. From 2003 to
2009, the population was increasing 2% on average per year due to rising
immigration.
a. Let P(t) represent the population of Iceland, where t is years after 2003.
Write an exponential function that models the country’s population.
b. Estimate the population in 2004 and round to the nearest whole number.
c. Estimate the population in 2008 and round to the nearest whole number.
d. Find the average rate of change of the country between 2004 and 2008.
Round to the nearest whole number and interpret your answer.
Sources: www.statice.is; www.pbs.org; www.earthobservatory.nasa.gov
6. Logarithmic Functions: On September 1, 1923, an 8.3 magnitude
earthquake struck the cities of Tokyo and Yokohama, Japan just a few
minutes before noon. The earthquake was given the name “The Great
Kanto Earthquake” due to the devastation of the Kanto region of Japan, in
which over 140,000 people died.
a. Find the intensity of the earthquake and express its intensity in terms
of that of a standard earthquake, that is, Io.
b. Compare its intensity with the 8.9 magnitude earthquake that
occurred on March 11, 2011 in Japan. Answer in a complete
sentence. Round answer to 3 decimal places.
Sources: www.eas.slu.edu; www.earthquakefacts.net
Kurt Overheiser, Julia Nudel, and Damion Hammock, Valencia College (2014), College Algebra
Math Problems with a Global Context #1
College Algebra (Acosta and Karwowski, 2012)
7. Topic??: The People’s Republic of China, commonly known as China, is
the most populous country in the world, with 1.33 billion people as of
2010. By 2030, China’s population is projected to reach a peak of 1.45
billion people and start declining, whereas India’s population is expected
to take over China to become the most densely populated country by
2040, with a projected population of 1.52 billion people.
Since the early 1970s, China’s economy has developed into a marketoriented one, playing a major role in the global economy. In 2008 the
global economic crisis had an effect on China’s Gross Domestic Product
(GDP) growth rate. Nevertheless, as of 2011, China was the world’s
largest exporter, and its economy is considered the second largest in the
world, only preceded by the United States. The function f(x) = -0.00262x4
+ 0.10432x3 - 1.33214x2 + 5.75396x + 4.86705 models the percent tof
change in China’s real economic growth rate, where x is the number of
years after 1990.
a. Use the given function to estimate the percent of change in China’s
real economic growth rate during the year 2008. Round to the
nearest whole number and answer in a complete sentence.
b. Graph the given function for 0  x  25. Label the axes and show
your window.
c. Use your graph to determine the year when China experienced the
lowest economic growth between 1995 and 2005. State the year and
the growth rate percentage. Round each answer to the nearest whole
number.
d. Estimate the year when China experienced a maximum economic
growth rate for the 2000 to 2009 time period.
Kurt Overheiser, Julia Nudel, and Damion Hammock, Valencia College (2014), College Algebra
Sources: www.cia.gov; www.chinability.com;
www.state.gov; www.tradingeconomics.com;
www.geography.about.com
Math Problems with a Global Context #1
College Algebra (Acosta and Karwowski, 2012)
8. Rational Functions: One of the greatest wonders of the world, the
Great Wall of China is approximately 5,500 miles long. It is actually a
collection of walls that follow the hills in the Mongolian plain. the Great
Wall of China was built over 2,000 years ago by Qin Shi Huangdi, the first
emperor of China, and the first set of walls were designed to protect the
Chinese Empire from invaders. It is estimated that if all the sections from
the different dynasties were to be counted, the total length would be
approximately 31,000 miles. Through the years, the wall has become
shorter due to natural erosion and human activity, and some of its original
sections are unrecognizable.
A group of college students are working on a movie set replicating a small
model of the Great Wall of China. They are using small Styrofoam bricks
that need to be painted and then assembled together over a large area of
synthetic turf. The amount of time, t, in minutes it takes them to construct
and build the wall varies directly with the number of bricks, b, and
inversely proportional to the number of students, s. Suppose it takes 45
minutes for 7 students to construct and assemble 50 bricks of the wall.
a. Find the constant of proportionality to 1 decimal place.
b. Find the equation of variation.
c. Determine the time it would take 12 students to construct and
assemble 100 bricks. Round your answer to 1 decimal place.
d. Determine the number of students if it took 2 hours for 200 bricks.
Round to the nearest whole number.
e. Determine the number of bricks constructed and assembled if it took
15 students 80 minutes. Round to the nearest whole number.
Kurt Overheiser, Julia Nudel, and Damion Hammock, Valencia College (2014), College Algebra
Sources: www.geography.com;
www.chinahighlights.com; www.travelchina.com;
www.great-wallofchinainfo.com
Math Problems with a Global Context #1
College Algebra (Acosta and Karwowski, 2012)
9. Linear Functions & Modeling: Yoga is an ancient
physical and spiritual discipline and branch of philosophy
that originated in India. Yoga began to grow in popularity
in the United States in the 1960s and is now considered
part of the mainstream of American culture. Meditation
Studio charges $12 per drop-in session, plus a one-time
fee of $17 for a special microfiber towel to place on top
of the floor mats for absorbing perspiration. Yoga
Retreat Studio charges $8 per drop-in session plus $33
for the microfiber towel. Let x represent the number of
sessions and y be the total cost for yoga lessons.
a. Write an equation for the total cost of membership to the
Meditation Studio.
b. Write an equation for the total cost of membership to the
Yoga Retreat Studio.
c. Solve the system of equations algebraically and interpret
the solution. Answer in a complete sentence.
d. If you wanted to take 9 yoga lessons in one of these two
studios, which will be more cost-effective? Answer in a
complete sentence.
e. If you only wanted to take 3 yoga lessons in one of these
two studios, which will be more cost-effective? Answer
in a complete sentence.
f.
Go to www.xe.com/currencyconverter/ and determine
what currency is used in India and what the conversion
rate is for 1 USD.
g. What would be the cost in Indian currency for the
answers to a and b?
h. The Sivandanda Yoga Vedanta Centre in Chennai, India
charges R1,500 as the monthly rate to take 30 beginner
classes. How many USD is that?
Kurt Overheiser, Julia Nudel, and Damion Hammock, Valencia College (2014), College Algebra
Math Problems with a Global Context #1
College Algebra (Acosta and Karwowski, 2012)
10. Exponential Decay: In Japan, an 8K Ultra High Definition 85inch television sells for 2,534,000 Japanese Yen (JPY) in 2014.
Electronics of this type depreciate in value between 20% - 30% per
year. If we assume this television will depreciate an average of
25% per year, what will the value (in JPY) be in the year 2024?
Note: 8K Ultra High Definition televisions are not yet available in
the U.S.
Follow up Thought/Discussion Questions:
a) Why is some technology and products available exclusively to
some countries while others wait to have it available?
b) For those unaccustomed to foreign currency, 2,534,000 JPY
may seem like a lot of money. Look up the current exchange rates
between the U.S. dollar and Japanese Yen. What do you think a
livable wage per hour in Japanese Yen might be?
Kurt Overheiser, Julia Nudel, and Damion Hammock, Valencia College (2014), College Algebra
Math Problems with a Global Context #1
College Algebra (Acosta and Karwowski, 2012)
11. Linear Regression: One World Trade Center (Freedom Tower) in
NYC will be the tallest building in the U.S. when it is completed in
2014. It will have 104 floors and stand 541 meters high. The
Shanghai Tower in Shanghai China is also projected to be
completed in 2014. It will have 121 floors and stand 632 meters
high.
In 2004, the tallest building in the world was Taipei 101 in Taipei
Taiwan. It has 101 floors and stands 509 meters high. In 2011, the
Abraj Al Bait Towers (Clock Tower) in Mecca Saudi Arabia was
completed and has 120 floors and stands 601 meters high. Use
the information given to construct a regression line where ___
represents the number of floors and ___ represents the height in
meters of each building.
Kurt Overheiser, Julia Nudel, and Damion Hammock, Valencia College (2014), College Algebra