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(Solved) 3 COLLEGE ALGEBRA - TRIGONOMETRY Business and Finance (MAT115) This course will start with a review of basic algebra (factoring, solving linear...

need solution 1. modeling unemployment rates data chapter solution. 2. rising gas price crisis: how fast and why? chapter solution and 3. price per square foot chapter solution. i need by tomorrow. please help me.

Business and Finance (MAT115) This course will start with a review of basic algebra (factoring, solving linear equations, and equalities, etc.) and
proceed to a study of polynomial, exponential, logarithmic, and trigonometric functions. These functions will
be used in applications involving simple mathematical
modeling where students will engage in inquiry activities aimed at improving critical thinking skills. title following page Modeling Unemployment Rates Data
Denise A. Carter
Department of Mathematics, Engineering, and Computer Science Objectives
To demonstrate to students that math is a part of their
daily lives and that the concepts learned in class are relevant to the real world. This lesson will show that actual
data taken from January to September 2008 unemployment rates are approximately linear. Linear functions
are encountered from Lesson 2 to Lesson 13 in the syllabus of College Algebra and Trigonometry (MAT115).
Through this activity, students are expected to achieve
the following:
• To understand the concept of a function and its role
in mathematical modeling of real-life problems • To know how to recognize a linear function • To be able to graph a linear function • To be able to write the equation of a linear function • To solve textbook applications of linear functions • To solve systems of linear equations in two variables
by using the graphical, elimination, and substitution methods • To learn the MAPLE commands for this activity • To read articles about unemployment rates Math Topics
Graphing linear equations, equation of
a line, applications of linear functions
Based on unemployment rates data
and news coverage in the Washington
Post and ABC News
When to Introduce
Week 10 (after introducing
measurements and plotting graphs)
Week 3
Activity Time Frame
From a week to a week-and-a-half Reflection
I am using economic current events that are pertinent in students’ lives to show the relevance
and importance of math. It is anticipated that students will become more aware about their
economic predicament and take a more active and aggressive role in their daily lives. It is also
expected that they will be able to translate the concepts to similar situations.
The students at first were somewhat intimidated by the project because it was the first major project and they did not know what to expect. But they later realized that all the preparation they
received from classwork, homework, and MAPLE labs was pertinent to the assignment.From the
students’ comments concerning the project, they seemed to have gained more respect for math
because they were able to see the learned concepts used in real situations.
Because this project was meant for ePortfolio, I expected students to demonstrate their abilities to
read, analyze, think critically, and communicate effectively. I have learned from my experience
that this seemingly daunting task makes many students anxious. In the future, I will introduce
reading material earlier, and prepare mini practice projects to make a smoother transition into
the first major project. Project Quantum Leap SAMPLER 143 Modeling Unemployment Rates Data
Activity Overview
This project should be introduced after Lesson 13 and after the MAPLE commands are learned.
This will be about three-and-a-half weeks into a twelve-week semester. The students are given a
week to a week-and-a-half to complete the project.
1. After Lesson 13, distribute “Modeling Unemployment Rates Data” Project Handout. Direct
students to (i) read the Washington Post and ABC News articles, and (ii) listen to Dan Arnell’s
report on the ABC News website.
2. Ask students to follow the instructions in the handout to (i) write a brief review of the Washington Post article and (ii) indicate what the hardest hit industries were, based on the ABC
News report.
3. In a computer lab, ask students to use MAPLE to analyze the unemployment rates data for
the months January through September 2008 provided in the handout. The instructor should
encourage collaborative learning, and offer necessary assistance.
4. As homework, ask students to verify the numerical results, and write a reflection based on
their quantitative analysis.
5. Collect the complete project, and ask students to deposit the electronic version on ePortfolio. Materials and Resources
Background information on the unemployment situation is given in the following articles: 144 • Handout • Reading #1: Irwin, N., & Rosenwald, M.S. (2008, October 23). Job losses accelerate, signaling
deeper distress. Washington Post. Retrieved January 30, 2009, from • Reading #2: Unemployment at 5 year high as U.S. loses 84,000 jobs.
Retrieved January 29, 2009, from
Story?id=5733848&page=1 (Listen to Dan Arnell’s report on 84,000 jobs slashed in August
2008.) • Unemployment data percentage rates can be obtained from the U.S. Misery Index (2008,
November 9). Retrieved January 29, 2009, from • PowerPoint presentations were used when teaching functions in general, linear functions,
and solving systems of linear functions. Handouts were also used to reinforce topics. Please
contact Dr. Denise A. Carter for these materials. LaGuardia Community College/CUNY Modeling Unemployment Rates Data
Handout: Modeling Unemployment Rates Data
Carter | Algebra and Trigonometry – Business and Finance (MAT115)
Due: _________________
Late papers will lose 10 points. Objective
To enhance the understanding of linear functions through the use of MAPLE and current newspaper articles on unemployment in the United States. Directions
Read the following articles: (i) Irwin, N., & Rosenwald, M.S. (2008, October 23). Job losses accelerate, signaling deeper distress attached to this handout and (ii) the ABC News Unemployment at
5-year high as U.S. loses 84,000 jobs. Listen to Dan Arnell’s report on 84,000 jobs slashed at http://
Use MAPLE to solve the following
1. Write a brief review of the Irwin & Rosenwald article. [25 points]
2. What industries does the ABC news article state were hit the hardest this time around? [15
3. The data in the table below gives the unemployment rates for the months January through
September 2008 (obtained from the U.S. Misery Index website:
[January = 1, February = 2, etc.]
Month Unemployment Percentage Rate 1 4.9 2 4.8 3 5.1 4 5.0 5 5.5 6 5.5 7 5.7 8 6.1 9 6.1 Make a scatter plot of the data. [20 points]
4. Find and graph the regression line that models the data above. Interpret the slope with
respect to the unemployment percentage rates. [20 points]
5. Assuming that this trend continues, use the model found in Question 3:
a. To predict the unemployment rate in July 2009. [8 points]
b. To find when the unemployment rate will be 10%. [12 points] Project Quantum Leap SAMPLER 145 Modeling Unemployment Rates Data
6. Based on your analysis, write a reflection essay. Consider the following guiding questions:
a. If the unemployment situation continues, what will the unemployment rate be at the
time you graduate from college?
b. What do you think the government should do to stop the job loss trend?
c. How do you remain competitive in this tough job market? 146 LaGuardia Community College/CUNY Modeling Unemployment Rates Data
Reading #1: Job Losses Accelerate
Carter | Algebra and Trigonometry – Business and Finance (MAT115)
Source: Irwin, N., & Rosenwald, M.S. (2008, October 23). Job losses accelerate, signaling deeper
distress. Retrieved January 30, 2009, from Employers are moving to aggressively cut jobs and reduce
costs in the face of the nation’s economic crisis, preparing
for what many fear will be a long and painful recession.
The labor market has been weak all year, with a
slow drip of workers losing their jobs each month. But
the deterioration of the job market is now emerging as a
driver of economic distress, according to a wide range of
data and anecdotal reports from corporate America.
In September, there were more mass layoffs –
instances in which employers slashed 50 or more jobs at
one time – than in any month since September 2001, the
Labor Department said yesterday. And nearly half a million Americans have filed new claims for unemployment
benefits in each of the past four weeks, the highest rate
of such claims since just after the terrorist attacks seven
years ago.
Anecdotal reports suggest that the hemorrhaging in the job market has only begun. Companies that
announced plans this week to cut jobs include Internet
company Yahoo (1,500 positions), pharmaceutical
company Merck (7,200), National City bank (4,000) and
Comcast, the cable company (300).
The weakening employment outlook is part of the
reason that investors have become more fearful of a deep,
prolonged recession – fears that led to yet another miserable day on Wall Street yesterday, with the Dow Jones
industrial average down 514 points, or 5.7 percent.
“The customers I’ve spoken to are all living under a
sense of fear,” said Paul Villella, chief executive of HireStrategy, a Reston company that matches employers and
workers. “They have very limited visibility into the future
and have a great degree of uncertainty, so they just want
to sit steady and be conservative in hiring.”
Villella and others who work with employers said
that for many companies, the pullback in hiring is not
a direct result of tightening credit. Rather, firms simply
don’t know whether their own customers will be affected
by the financial crisis; as a result, they want to hold their
breath and delay hiring decisions until they have a better
sense of the future. The nation has shed jobs every month this year, but
at a slower overall pace than in past economic downturns. The slide accelerated in late summer, with declines
similar to those in past recessions. Last month, employers shed 159,000 jobs, the most this year and more than
the average number of monthly job losses in the terrible
labor markets of 2001 and 2002.
More obscure indicators monitored by economists
at the Federal Reserve and in the private sector also show
an inflection point in late summer. For example, employers had 214,000 fewer job openings in August than in
July, according to a Labor Department report. Over the
past year, the number of openings dropped by a more
modest average of 74,000 per month.
Indeed, many companies are imposing hiring
freezes. Such moves don’t often get the kind of headlines
that layoffs do, but because they shrink the number of
places people can turn to for jobs, they still hurt the
economy. Project Quantum Leap SAMPLER 147 Modeling Unemployment Rates Data
VMware, a Palo Alto, Calif., software company, is
one firm that has curbed hiring. Earlier this week, after
reporting third-quarter earnings that beat Wall Street’s
expectations, VMware told analysts on a conference
call that despite a 32 percent jump in revenue, a “hiring
pause” had been imposed for all jobs except critical ones.
“We are just being conservative,” VMware spokeswoman Mary Ann Gallo said yesterday.
The nation’s unemployment rate was 6.1 percent
last month, not astronomical by historical standards.
But the rate was up from 5 percent in April, and many
forecasters now expect it to hit 7 percent or more by the
end of this downturn.
The construction and manufacturing sectors have
been losing jobs for more than a year. But lately, job
losses have begun or accelerated in a wide range of other
fields. Retailers, stung by less consumer spending, cut
87,000 jobs in the three months ended in September.
Employment services shed 100,000 positions in that
span, reflecting the fact that companies are slashing
temporary jobs. The leisure and hospitality industry cut
51,000 jobs, as people had less money to stay in hotels
and eat in restaurants.
In the greater Los Angeles area, Manpower, one of
the nation’s largest temp agencies, has noticed a steady
increase in job seekers since early September. Paul
Holley, a spokesman for the company, said there are
more applicants for fewer openings and better-qualified
candidates seeking work.
What’s particularly noteworthy, Holley said, is
what’s happening in Phoenix. Job applications have held
steady, but since September more applicants have had
backgrounds in general labor and warehouse distribution. That’s unusual because warehouse and logistics
jobs usually hold steady in the fall to support retailing for
holiday shopping.
Randstad USA, another large temp agency, reports
that job applications are up in the Tucson area and that
the firm is even getting inquires from people who still
have jobs. “In general, a lot of people seem to be insecure
about their current jobs even if they are still employed,”
said Emily Cline, Randstad’s area vice president for
As reports of layoffs continue to pile up around the
country, executives at Randstad said they have noticed a
shift in psychology among job seekers.
“Employees are much more willing to work extra
hours and to take on additional duties to enhance job 148 LaGuardia Community College/CUNY security and improve their employability,” said Eric
Buntin, managing director for marketing and operations
at Randstad. “In a changing market, they know that’s a
valuable resource.”
They are also willing to make less money, even as
the cost of living goes up. Cline said some call center jobs
that were paying $9 an hour in the Tucson area last year
are now paying $8.50. “Their option becomes to take the
job or not have the job,” she said.
With workers losing their leverage to negotiate
raises, there could be greater downward pressure on
wages, which in turn could drive down overall economic
growth. Workers are already having a hard time getting
raises; inflation-adjusted pay for non-managerial workers
fell 1.9 percent in the year ended in September, according
to the Labor Department.
Staff writer Michael A. Fletcher in Cleveland contributed to
this report. Modeling Unemployment Rates Data
Reading #2: Unemployment at 5-Year High
Carter | Algebra and Trigonometry – Business and Finance (MAT115)
Source: Irwin, N., & Rosenwald, M.S. (2008, October 23). Job losses accelerate, signaling deeper
distress. Retrieved January 30, 2009, from
article/2008/10/22/AR2008102203709_pf.html Unemployment at 5-Year High as U.S. Loses 84,000 Jobs
The Job Losses Were Higher Than Economists Expected
Sept. 5, 2008 WASHINGTON (AP) -- The U.S.’s unemployment rate
zoomed to a five-year high of 6.1 percent in August as
employers slashed 84,000 jobs, dramatic proof of the
mounting damage a deeply troubled economy is inflicting on workers and businesses alike.
The Labor Department’s report, released Friday,
showed the increasing toll the housing, credit and financial crises are taking on the economy. How is the Economy Treating You? Tell ABC News
The report was sure to rattle Wall Street again. All the
major stock indexes tumbled into bear territory Thursday as investors lost hope of a late-year recovery. With
the employment situation deteriorating, there’s growing
worry that consumers will recoil, throwing the economy
into a tailspin later this year or early next year.
The jobless rate jumped to 6.1 percent in August,
from 5.7 percent in July. And, employers cut payrolls for
the eighth month in a row. Job losses in June and July
turned out to be much deeper. The economy lost a whopping 100,000 jobs in June and another 60,000 in July,
according to revised figures. Previously, the government
reported job losses at 51,000 in each of those months.
The latest snapshot was worse than economists were
forecasting. They were predicting payrolls would drop by
around 75,000 in August and the jobless rate to tick up
a notch, to 5.8 percent. The grim news comes as the race
for the White House kicks into high gear. The economy’s
troubles are Americans’ top worry.
Wachovia Corp., Ford Motor Co., Tyson Foods Inc.
and Alcoa Inc. were among the companies announcing
job cuts in August. GMAC Financial Services this week
said it would lay off 5,000 workers.
Job losses in August were widespread. Factories cut 61,000 jobs, construction firms eliminated 8,000 jobs,
retailers axed 20,000 slots, professional and business services slashed 53,000 positions and leisure and hospitality
got rid of 4,000. Those losses swamped employment
gains in the government, education and health.
Job losses at all private employers -- not including
government -- came to 101,000 in August.
The government said workers age 25 and older
accounted for all the increase in unemployment in
Workers saw wage gains in August, however.
Average hourly earning rose to $18.14 in August, a
0.4 percent increase from July. Economists were forecasting a 0.3 percent gain. Over the past year, wages have
grown 3.6 percent, but paychecks aren’t stretching as far
because of high food and energy prices.
Caught between dueling concerns of slow growth
and inflation, the Fed is expected to leave a key interest
rate alone at 2 percent when it meets next on Sept. 16 and
probably through the rest of this year. Concerned about
inflation, the Fed at its last two meetings didn’t budge
the rate. Before that, though, the Fed had aggressively cut
rates to shore up the economy.
With the Fed on the sidelines, Democratic presidential nominee Barack Obama has called for a second
round of government stimulus, while his Republican
rival John McCain has favored free-trade and other business measures to spur the economy.
Copyright © 2009 ABC News Internet Ventures Project Quantum Leap SAMPLER 149 Car Buyers in Asia Gordon Crandall
Department of Mathematics, Engineering, and Computer Science Objectives
Students will read an article that describes in “grassroots” terms the arrival of new car dealers in rural
China and the consequences of vehicle ownership
where scant years before, the bicycle provided the sole
means of local transportation. Apart from sociological “color,” data is given on the explosive growth of
vehicle sales in China and in India in the past several
years, along with the (slight) decline in vehicle sales in
the United States. Students will model this data using
exponential, quadratic, and linear models, and they
will make predictions on sales volume in future years.
Coming later in the semester – at the point of introduction of exponential functions – the assignment reviews
linear and quadratic functions, and serves as a capstone activity on the types of growth over time featured
in the course. Math Topics
Linear, quadratic, exponential
Review, synthesis
Based on New York Times article
describing bittersweet arrival of car
dealerships in rural China
When to Introduce
Week 10
Activity Time Frame
Two weeks Reflection
Discussion of the dynamic surge in Chinese and Indian
car sales could lead naturally to cautionary tales of
increased competition for finite petro-resources and
increasing emissions of greenhouse gases. With prior
exposure to curve fitting/modeling, students found this activity engaging. Making the graphs by
hand or with Excel is visually appealing and students enjoyed creating the final product. These
calculations were more natural “live” versions of the drier Educo textbook problems. However,
quantitative issues are not really the main thrust of this article, although it does offer eyeopening data on the dynamic growth of automobile ownership in Asia. Instructors selecting this
activity should not deprive themselves of class discussion on the impact of vehicle ownership on
insulated traditional cultures. The article evokes powerfully the warm spring winds of entrepreneurial capitalism, followed – ironically – by the destructive 2008 summer earthquake in Hunan
and the crash of world markets in the early fall of 2008. Activity Overview
Week 10 (Period 1): Activity handout and “cultural” discussion (30 minutes) Week 10 (Period 2): Review data entry and regression modeling features for TI-83 or Excel (40
minutes) Week 11 (Period 1): Hints and straggler management (20 minutes) Week 11 (Period 2): Wrap-up (15 minutes) Project Quantum Leap SAMPLER 151 Car Buyers in Asia
Materials and Resources 152 • Handout • Reading: Bradsher, K. (2008, April 24). With first car, a new life in China. New York
Times. Retrieved January 30, 2009, from
worldbusiness/24firstcar.html • TI-83 graphing calculator (or equivalent modeling tool, such as Excel) LaGuardia Community College/CUNY Car Buyers in Asia
Handout: Car Buyers in Asia
Crandall | Algebra and Trigonometry – Business and Finance (MAT115)
Due: _________________
Late papers will lose 10 points. Car Buyers in Asia and in the U.S.
1. The table below gives data on passenger vehicle sales (cars, minivans, and sport utility
vehicles in China.
Vehicles sold (in millions) 2000 2001 2002 2003 2004 2005 2006 2007 2008 .6 .8 1.2 2.2 2.4 3.1 4.2 5.3 6.1 a. Taking the year 2000 as t=0, make a scatter plot of the data using an Excel spreadsheet
or a piece of graph paper.
b. Using Excel (or a TI-83 graphing calculator) enter years since 2000 as x-values and
vehicle sales in millions as y-values, and fit the data to an exponential equation.
c. Using the equation in b), predict vehicle sales volume in China in 2015. What about
d. In what year will sales volume reach 12 million vehicles?
2. The table below gives similar data on vehicle sales in India.
Year 2003 2004 2005 2006 2007 2008 0.8 1.0 1.2 1.4 1.6 2.0 Vehicles sold (in millions) a. Taking the year 2003 as t=0, make a scatter plot of the data using an Excel spreadsheet
or a piece of graph paper.
b. Using Excel (or a TI-83 calculator), enter years since 2003 as x-values and vehicle sales in
millions as y-values, and fit the data to a quadratic best-fit model.
c. Using your equation in b), predict the sales volume in India in 2015. What about 2030?
d. In what year will sales volume in India reach 12 million vehicles?
3. Year
Vehicles sold (in millions) 2000 2001 2002 2003 2004 2005 2006 2007 2008 13.8 13.5 13.3 13.0 13.1 13.1 12.8 12.4 12.0 The table below gives data on vehicle sales in the United States.
a. Taking the year 2000 as t=0, make a scatter plot of the data using an Excel spreadsheet
or a piece of graph paper.
b. Using Excel (or a TI-83 graphing calculator), enter years since 2000 as x-values and
vehicle sales in millions in the U.S. as y-values; find the equation of the best line through
the data.
Project Quantum Leap SAMPLER 153 Car Buyers in Asia
c. Using the linear equation that you found in b), predict the sales volume in 2015. What
about 2030?
4. Assuming that vehicle sales in India continue to grow quadratically, and that vehicle sales
in the United States continue to decrease linearly, in what year will the sales volume in these
two countries be equal? What is the vehicle sales volume at this time? Do you think that this
will ever happen? What assumptions must be questioned? Explain.
5. According to the article, “With First Car, a New Life in China,” are Chinese domestic carmakers like Geely and Chery the main beneficiaries of the explosive growth in vehicle sales in
China? Explain your answer.
6. Based on the reading, write a brief essay discussing how the status of automobile ownership
is beginning to reconfigure traditional folkways in rural China.
7. Discuss the environmental consequences of the explosive growth of car sales in countries
like India and China in terms of emissions/greenhouse gases and in terms of competition for
(ultimately finite) energy resources. 154 LaGuardia Community College/CUNY Car Buyers in Asia
Reading: Car Buyers in Asia
Crandall | Algebra and Trigonometry – Business and Finance (MAT115)
Source: Bradsher, K. (2008, April 24). With first car, a new life in China. New York Times. Retrieved
January 30, 2009, from
html. SHUANG MIAO, China – Li Rifu packed a lot of emotional freight into his first car. Mr. Li, a 46-year-old farmer
and watch repairman, and his wife secretly hoped a car
would better the odds of their sons, then 22 and 24, finding girlfriends, marrying and producing grandchildren.
A year and a half later, the plan seems to be working. After Mr. Li purchased his Geely King Kong for the
equivalent of $9,000, both sons quickly found girlfriends.
His older son has already married, after a short courtship
that included a lot of cruising in the family car, where the
couple stole their first furtive kisses.
“It’s more enclosed, more clandestine,” said Li Fengyang, Mr. Li’s elder son, during a recent family dinner, as
his bride blushed deeply.
Western attention to...


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