Math Problems with a Global Context #2
College Algebra in Context, 4th Edition (Harshbarger, Yocco)
43. Box Office Revenue Worldwide box office revenue for all films reached $29.9 billion in
2009, up 7.6% over the 2008 total. U.S./Canada and international box office revenues in U.S.
dollars were both up significantly over the 2005 total.
Worldwide Box Office Revenue (US$ billions)
2005
2006
U.S./Canada
8.8
9.2
International
14.3
16.3
Worldwide
23.1
25.5
(Source: Motion Picture Association of America)
2007
9.1
16.6
26.3
2008
9.6
18.1
27.8
2009
10.6
19.3
29.9
a. Let x = the number of years after 2000 and draw a scatter plot of the U.S./Canada
data.
b. Find and graph the linear function that is the best fit for the U.S./Canada data.
y = 0.4x – 6.66
c. Let x = the number of years after 2000 and draw a scatter plot of the international
data.
d. Find and graph the liner function that is the best fit for the international data.
y
= 1.18x + 8.66
e. If the models are accurate, will U.S./Canada box office revenue ever reach the level
of international box office revenue? No
EXAMPLE 5 China’s Manufacturing
Figure 2.29 shows the size of the
manufacturing sector of China and
that of the United States in this
century. Suppose these graphs
for China and the United States
can be modeled by the functions.
𝑦 = 0.158𝑥 −
0.0949 and 𝑦 = 0.037𝑥 + 1.477
respectively, with x representing
the years after 2000 and y
representing the sizes of the
manufacturing sector in trillions of
2005 dollars. Find the year during
which China reaches the United
States on its way to becoming the
world’s largest manufacturer.
Kurt Overheiser, Julia Nudel, and Damion Hammock, Valencia College (2014), College Algebra
Math Problems with a Global Context #2
College Algebra in Context, 4th Edition (Harshbarger, Yocco)
SOLUTION
Chinas manufacturing sector reaches that of the United States when the y-values of the two
models are equal, so we solve the following system by substitution:
{𝑦 = 0.158𝑥 − 0.0949
{𝑦 = 0.0.37𝑥 + 1.477
0. 158𝑥 – 0.0949 = 0.037𝑥 + 1.477
0.121𝑥 = 1.5719
𝑥 = 12.99 ≈ 13
Thus, the size of China’s manufacturing sector is estimated to reach that of the United States in
2013. We can check the solution graphically by graphing the two functions and using
INTERSECT on a graphing calculator. (See Figure 2.30.)
45. Shoe Sizes A women’s shoe that is size x in Japan is size s(x) in the United States, where
𝑠(𝑥) = 𝑥 − 17. A women’s shore that is size x in the United States is size p(x) in Britain, where
𝑝(𝑥) = 𝑥 − 1.5. Find a function that will convert Japanese shoe size to Continental shoe size.
𝑝(𝑠(𝑥)) = 𝑥 − 18.5
46. Shoe Sizes A man’s shoe that is size x in Britain is size d(x) in the United States, where
𝑑(𝑥) = 𝑥 + .05. A man’s shoe that is size x in the Unites States is size t(x) in Continental size,
where 𝑡(𝑥) = 𝑥 + 34.5. Find a function that will convert shoe size to Continental shoe size.
𝑡(𝑑(𝑥)) = 𝑥 − 35
47. Exchange Rates On March 11, 2011, each Japanese yen was worth 0.34954 Russian ruble
and each Chilean peso was worth 0.171718 Japanese yen. Find the value of 100 Chilean pesos
in Russian Rubles on March 11, 2011. Round the answer to two decimal places. 6.00 Russian
Rubles
48. Exchange Rates On March 11, 2011, each euro was worth 1.3773 U.S. dollars and each
Mexican peso was worth 0.06047 euro. Find the value of 100 Mexican pesos in U.S. dollars.
$8.53
61. Japan Tsunami In May of 2008, an earthquake measuring 6.8 on the Richter scale struck
near the east coast of Honshu, Japan. In March of 2011, an earthquake measuring 9.0 struck
that same region, causing a devastating tsunami that killed thousands of people. The 2011
earthquake was how many times as intense as the one in 2008? 158.5 times as intense
Kurt Overheiser, Julia Nudel, and Damion Hammock, Valencia College (2014), College Algebra
Math Problems with a Global Context #2
College Algebra in Context, 4th Edition (Harshbarger, Yocco)
71. Deforestation The number of square miles per year of rain forest destroyed in Brazil is given
by 𝑦 = 4899.7601(1.0468𝑥 ), where x is the number of years from 1990. In what year did 6447
square miles get destroyed, according to the model? 1996
17. Japanese Economy The economy of Japan is the third largest in the world, after those of the
United States and the People’s Republic of China. With average growth rates of 10% in the
1960s, 5% in the 1970s, and 4% in the 1980s, Japan was able to establish and maintain itself
as the world’s second largest economy from 1968 until 2010. However, Japan’s economy was
disrupted in early 2011 because of the earthquake and tsunami. The percent changes in gross
domestic product (GDP) for each year since 1997 are given in the figure.
a. Find a quartic function that models the data, where x equals the number of years
after 1990 and y is the percent change. 𝑦 = 0.0041𝑥 4 − 0.222𝑥 3 + 4.287𝑥 2 −
34.840 + 101.342
b. Use the model to estimate the percent change in GDP for 2012. 5.06% (using the
unrounded model)
c. Does the model appear to be accurate after 2013? Why or why not? No: percent
change for 2014 is predicted to be 23.50% which is unlikely.
Kurt Overheiser, Julia Nudel, and Damion Hammock, Valencia College (2014), College Algebra