Problem 1
You work on an FBI team investigating “Bitcoin,” a digital form of currency that has been the subject
of extensive scrutiny by international financial and law enforcement authorities. It was the currency
used for transactions in the “Silk Road” dark Web drug-trafficking markets, which were shut down by
law enforcement officials in late 2013 and again in late 2014
(http://www.usatoday.com/story/news/nation/2014/11/06/feds-shut-down-silk-road-copycat/18591
155/).
The average market price in US dollars of one Bitcoin from January 2014 (just after the first “Silk
Road” incident) through July 2016 has fluctuated significantly as indicated in the following table of
values:
Date
x-value
Months since
January 2014
y-value
Average US$ market price
per Bitcoin
January, 2014 0 805
April, 2014 3 462
July, 2014 6 651
October, 2014 9 386
January, 2015 12 316
April, 2015 15 245
July, 2015 18 261
October, 2015 21 239
January, 2016 24 434
April, 2016 27 419
July, 2016 30 679
October, 2016 33 615
(https://bitcoinaverage.com/en/bitcoin-price/btc-to-usd)
a) Use the Desmos graphing calculator (https://www.desmos.com/calculator) to construct a scatter
plot for the data given from January 2014 to April 2015. Label the axes of the scatter plot to
reflect the information given in the table.
i) Determine the slope of the line through the data points given in January 2014 and April 2015.
Write the slope in decimal form, rounding to the nearest tenth if necessary.
ii) Write an equation in slope-intercept form of the line through the data points given in January
2014 and April 2015.
Math 037 Problem-Solving Applications (Week 5)
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iii) Add the line with equation found in part (ii) to your graph of the scatter plot. Does this line
appear to be a good model for the data in this scatter plot? Why or why not?
b) Use the Desmos graphing calculator (https://www.desmos.com/calculator) to construct a scatter
plot for the data given from January 2014 to April 2015. Label the axes of the scatter plot to
reflect the information given in the table.
i) A possible linear model for the data given from January 2014 to April 2015 is given by the
equation y = -33x + 730. Add that line to your graph of the scatter plot.
ii) Identify the x-intercept of the line drawn in part (i). Explain in a sentence or two what the
x-intercept means in the context of this linear model.
c) Use the Desmos graphing calculator (https://www.desmos.com/calculator) to construct a scatter
plot for the data given from October 2014 to October 2015. Label the axes of the scatter plot to
reflect the information given in the table.
i) Determine the slope of the line through the data points given in October 2014 and October
- Write the slope in decimal form, rounding to the nearest tenth if necessary.
ii) Write an equation in slope-intercept form of the line through the data points given in October
2014 and October 2015.
iii) Add the line with equation found in part (ii) to your graph of the scatter plot. Does this line
appear to be a good model for the data in this scatter plot? Why or why not?
d) Use the Desmos graphing calculator (https://www.desmos.com/calculator) to construct a scatter
plot for the data given from October 2014 to October 2015. Label the axes of the scatter plot to
reflect the information given in the table.
i) A possible linear model for the data given from October 2014 to October 2015 is given by the
equation y = -12x + 460. Add that line to your graph of the scatter plot.
ii) Identify the x-intercept of the line drawn in part (i). Explain in a sentence or two what the
x-intercept means in the context of this linear model.
e) Use the Desmos graphing calculator (https://www.desmos.com/calculator) to construct a scatter
plot for the data given from October 2015 to October 2016. Label the axes of the scatter plot to
reflect the information given in the table.
i) Determine the slope of the line through the data points given in October 2015 and October - Write the slope in decimal form, rounding to the nearest tenth if necessary.
Math 037 Problem-Solving Applications (Week 5)
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ii) Write an equation in slope-intercept form of the line through the data points given in October
2015 and October 2016.
iii) Add the line with equation found in part (ii) to your graph of the scatter plot. Does this line
appear to be a good model for the data in this scatter plot? Why or why not?
f) Use the Desmos graphing calculator (https://www.desmos.com/calculator) to construct a scatter
plot for the data given from October 2015 to October 2016. Label the axes of the scatter plot to
reflect the information given in the table.
i) A possible linear model for the data given from October 2015 to October 2016 is given by the
equation y = 33x – 405. Add that line to your graph of the scatter plot.
ii) Identify the x-intercept of the line drawn in part (i). Explain in a sentence or two what the
x-intercept means in the context of this linear model.
g) Use the Desmos graphing calculator (https://www.desmos.com/calculator) to construct a scatter
plot for all of the data given from January 2014 to October 2016. Label the axes of the scatter
plot to reflect the information given in the table.
i) Based on the scatter plot, do the data points appear to follow a linear model, a curvilinear
model, or neither?
ii) If the data relation appears to be linear, find the slope of the line through the first and last
data points in the table (January 2014 and October 2016) and explain the meaning of that
slope in the context of the problem.
iii) If the data relation appears to be non-linear, discuss in a few sentences some possible reasons
for the shape of the scatter plot shown.
Math 037 Problem-Solving Applications (Week 5)
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Problem 2
As a gerontologist, you are studying the changes in rate of heart disease among the elderly over time.
To gather background information, you start with a visit to the website of the Centers for Disease
Control and Prevention (CDC). On the CDC website, you find the table below, which displays the
age-adjusted death rate (per 1000 US standard population) due to heart disease from 1900 through
2010.
Year
x
Years since
1900
y
Age-adjusted death rate due to
heart disease (per 1000 standard
US population)
1900 0 2.65
1910 10 3.45
1920 20 3.75
1930 30 4.68
1940 40 5.59
1950 50 5.89
1960 60 5.59
1970 70 4.93
1980 80 4.12
1990 90 3.32
2000 100 2.58
2010 110 1.79
(https://data.cdc.gov/NCHS/NCHS-Age-adjusted-Death-Rates-for-Selected-Major-C/6rkc-nb2q)
a) Use the Desmos graphing calculator (https://www.desmos.com/calculator) to construct a scatter
plot for the data given from 1900 to 1950 . Label the axes of the scatter plot to reflect the
information given in the table.
i) Determine the slope of the line through the data points given in 1900 and 1950. Write the
slope in decimal form, rounding to the nearest hundredth if necessary.
ii) Write an equation in slope-intercept form of the line through the data points given in 1900
and 1950.
iii) Add the line with equation found in part (ii) to your graph of the scatter plot. Does this line
appear to be a good model for the data in this scatter plot? Why or why not?
Math 037 Problem-Solving Applications (Week 5)
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b) Use the Desmos graphing calculator (https://www.desmos.com/calculator) to construct a scatter
plot for the data given from 1900 to 1950. Label the axes of the scatter plot to reflect the
information given in the table.
i) A possible linear model for the data given from 1900 to 1950 is given by the equation
y = 0.07x + 2.65. Add that line to your graph of the scatter plot.
ii) Based on the equation given in part (i) what would the age-adjusted rate of heart disease be
in the year 2010?
iii) Compare your answer to (ii) with the actual age-adjusted rate of heart disease in the year - Is the linear model given in part (i) a reasonable approximation over the entire period
of time shown in the table? Why or why not?
c) Use the Desmos graphing calculator (https://www.desmos.com/calculator) to construct a scatter
plot for the data given from 1950 to 2000 . Label the axes of the scatter plot to reflect the
information given in the table.
i) Determine the slope of the line through the data points given in 1950 and 2000. Write the
slope in decimal form, rounding to the nearest hundredth if necessary.
ii) Write an equation in slope-intercept form of the line through the data points given in 1950
and 2000.
iii) Add the line with equation found in part (ii) to your graph of the scatter plot. Does this line
appear to be a good model for the data in this scatter plot? Why or why not?
d) Use the Desmos graphing calculator (https://www.desmos.com/calculator) to construct a scatter
plot for the data given from 1950 to 2000. Label the axes of the scatter plot to reflect the
information given in the table.
i) A possible linear model for the data given from 1950 to 2000 is given by the equation
y = -0.07x + 9.6. Add that line to your graph of the scatter plot.
ii) Based on the equation given in part (i) what would the age-adjusted rate of heart disease be
in the year 2010?
iii) Compare your answer to (ii) with the actual age-adjusted rate of heart disease in the year - Is the linear model given in part (i) a reasonable approximation over the entire period
of time shown in the table? Why or why not?
e) Use the Desmos graphing calculator (https://www.desmos.com/calculator) to construct a scatter
plot for the data given from 1930 to 1970. Label the axes of the scatter plot to reflect the
information given in the table.
Math 037 Problem-Solving Applications (Week 5)
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i) Determine the slope of the line through the data points given in 1940 to 1960. Write the
slope in decimal form, rounding to the nearest hundredth if necessary.
ii) Write an equation in slope-intercept form of the line through the data points given in 1940
and 1960.
iii) Add the line with equation found in part (ii) to your graph of the scatter plot. Does this line
appear to be a good model for the data in this scatter plot? Why or why not?
f) Use the Desmos graphing calculator (https://www.desmos.com/calculator) to construct a scatter
plot for the data given from 1930 to 1970. Label the axes of the scatter plot to reflect the
information given in the table.
i) A possible linear model for the data given from 1930 to 1970 is given by the equation
y = 0.005x + 5.086. Add that line to your graph of the scatter plot.
ii) Based on the equation given in part (i) what would the age-adjusted rate of heart disease be
in the year 2010?
iii) Compare your answer to (ii) with the actual age-adjusted rate of heart disease in the year - Is the linear model given in part (i) a reasonable approximation over the entire period
of time shown in the table?
g) Use the Desmos graphing calculator (https://www.desmos.com/calculator) to construct a scatter
plot for all of the data given from 1900 to 2010. Label the axes of the scatter plot to reflect the
information given in the table.
i) Based on the scatter plot, do the data points appear to follow a linear model, a curvilinear
model, or neither?
ii) If the data relation appears to be linear, find the slope of the line through the first and last
data points in the table (1900 and 2010) and explain the meaning of that slope in the context
of the problem.
iii) If the data relation appears to be non-linear, discuss in a few sentences some possible reasons
for the shape of the scatter plot shown.
Math 037 Problem-Solving Applications (Week 5)
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Problem 3
As a new lawyer in the Antitrust Division of the US Government’s Department of Justice, you are
researching the number of cases filed against individuals suspected of violating US antitrust laws in
recent years.
Below is a table that lists the number of criminal cases filed against individuals by the Justice
Department’s Antitrust Division annually, from 2006 to 2015
(https://www.justice.gov/atr/criminal-enforcement-fine-and-jail-charts):
Year
x
Years since 2006
y
Annual number of cases filed
against individuals
2006 0 37
2007 1 47
2008 2 59
2009 3 65
2010 4 63
2011 5 82
2012 6 63
2013 7 34
2014 8 44
2015 9 66
(https://www.justice.gov/atr/criminal-enforcement-fine-and-jail-charts)
a) Use the Desmos graphing calculator (https://www.desmos.com/calculator) to construct a scatter
plot for the data given from 2006 to 2009. Label the axes of the scatter plot to reflect the
information given in the table.
i) Determine the slope of the line through the data points given in 2006 and 2009. Write the
slope in decimal form, rounding to the nearest tenth if necessary.
ii) Write an equation in slope-intercept form of the line through the data points given in 2006
and 2009.
iii) Add the line with equation found in part (ii) to your graph of the scatter plot. Does this line
appear to be a good model for the data in this scatter plot? Why or why not?
Math 037 Problem-Solving Applications (Week 5)
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b) Use the Desmos graphing calculator (https://www.desmos.com/calculator) to construct a scatter
plot for the data given from 2006 to 2009. Label the axes of the scatter plot to reflect the
information given in the table.
i) A possible linear model for the data given from 2006 to 2009 is given by the equation
y = 9.6x + 37.6. Add that line to your graph of the scatter plot.
ii) Based on the equation given in part (i) how many antitrust cases would be filed against
individuals in 2015?
iii) Compare your answer to (ii) with the actual number of antitrust cases filed against individuals
in 2015. Is the linear model given in part (i) a reasonable approximation over the entire
period of time shown in the table? Why or why not?
c) Use the Desmos graphing calculator (https://www.desmos.com/calculator) to construct a scatter
plot for the data given from 2011 to 2013 . Label the axes of the scatter plot to reflect the
information given in the table.
i) Determine the slope of the line through the data points given in 2011 and 2013. Write the
slope in decimal form, rounding to the nearest tenth if necessary.
ii) Write an equation in slope-intercept form of the line through the data points given in 2011
and 2013.
iii) Add the line with equation found in part (ii) to your graph of the scatter plot. Does this line
appear to be a good model for the data in this scatter plot? Why or why not?
d) Use the Desmos graphing calculator (https://www.desmos.com/calculator) to construct a scatter
plot for the data given from 2011 to 2013 . Label the axes of the scatter plot to reflect the
information given in the table.
i) A possible linear model for the data given from 2011 to 2013 is given by the equation
y = -24x + 204. Add that line to your graph of the scatter plot.
ii) Based on the equation given in part (i) how many antitrust cases would be filed against
individuals in 2015?
iii) Compare your answer to (ii) with the actual number of antitrust cases filed against individuals
in 2015. Is the linear model given in part (i) a reasonable approximation over the entire
period of time shown in the table? Why or why not?
Math 037 Problem-Solving Applications (Week 5)
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e) Use the Desmos graphing calculator (https://www.desmos.com/calculator) to construct a scatter
plot for the data given from 2013 to 2015. Label the axes of the scatter plot to reflect the
information given in the table.
i) Determine the slope of the line through the data points given in 2013 and 2015. Write the
slope in decimal form, rounding to the nearest tenth if necessary.
ii) Write an equation in slope-intercept form of the line through the data points given in 2013
and 2015.
iii) Add the line with equation found in part (ii) to your graph of the scatter plot. Does this line
appear to be a good model for the data in this scatter plot? Why or why not?
f) Use the Desmos graphing calculator (https://www.desmos.com/calculator) to construct a scatter
plot for the data given from 2013 to 2015. Label the axes of the scatter plot to reflect the
information given in the table.
i) A possible linear model for the data given from 2013 to 2015 is given by the equation
y = 16x – 80 Add that line to your graph of the scatter plot.
ii) Identify the x-intercept of the line drawn in part (i). Explain in a sentence or two what the
x-intercept means in the context of this linear model.
g) Use the Desmos graphing calculator (https://www.desmos.com/calculator) to construct a scatter
plot for all of the data given from 2006 to 2015. Label the axes of the scatter plot to reflect the
information given in the table.
i) Based on the scatter plot, do the data points appear to follow a linear model, a curvilinear
model, or neither?
ii) If the data relation appears to be linear, find the slope of the line through the first and last
data points in the table (2006 and 2015) and explain the meaning of that slope in the context
of the problem.
iii) If the data relation appears to be non-linear, discuss in a few sentences some possible reasons
for the shape of the scatter plot shown.
Math 037 Problem-Solving Applications (Week 5)
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Problem 4
As a counselor in a college wellness center, you are aware that studies have shown a growing number
of college students are seeking counseling services for a variety of reasons, including depression,
anxiety, and relationship problems. You are interested in studying how the trends at your college
reflect national trends. You begin by examining the following table that lists the percentage of US
college students presenting with depression as their main reason for seeking counseling from 2007
through 2013
(http://www.apa.org/monitor/2014/09/cover-pressure.aspx):
Year
x
Years
since
2007
y
Percent of all US college students seeking
counseling who present with depression as
main reason for counseling (%)
2007 0 39.5
2008 1 37.2
2009 2 37.7
2010 3 38.0
2011 4 37.2
2012 5 36.3
2013 6 39.5
(http://www.apa.org/monitor/2014/09/cover-pressure.aspx)
a) Use the Desmos graphing calculator (https://www.desmos.com/calculator) to construct a scatter
plot for the data given from 2007 to 2010. Label the axes of the scatter plot to reflect the
information given in the table.
i) Determine the slope of the line through the data points given in 2007 and 2010. Write the
slope in decimal form, rounding to the nearest tenth if necessary.
ii) Write an equation in slope-intercept form of the line through the data points given in 2007
and 2010.
iii) Add the line with equation found in part (ii) to your graph of the scatter plot. Does this line
appear to be a good model for the data in this scatter plot? Why or why not?
Math 037 Problem-Solving Applications (Week 5)
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b) Use the Desmos graphing calculator (https://www.desmos.com/calculator) to construct a scatter
plot for the data given from 2007 to 2010. Label the axes of the scatter plot to reflect the
information given in the table.
i) A possible linear model for the data given from 2007 to 2010 is given by the equation
y = -0.4x + 38.7. Add that line to your graph of the scatter plot.
ii) Based on the equation given in part (i) what percent of all US college students who seek
counseling present with depression as the main reason for counseling in the year 2013?
iii) Compare your answer to (ii) with the actual percent shown in the table for 2013. Is the linear
model given in part (i) a reasonable approximation over the entire period of time shown in the
table? Why or why not?
c) Use the Desmos graphing calculator (https://www.desmos.com/calculator) to construct a scatter
plot for the data given from 2010 to 2013 . Label the axes of the scatter plot to reflect the
information given in the table.
i) Determine the slope of the line through the data points given in 2010 and 2013. Write the
slope in decimal form, rounding to the nearest tenth if necessary.
ii) Write an equation in slope-intercept form of the line through the data points given in 2010
and 2013.
iii) Add the line with equation found in part (ii) to your graph of the scatter plot. Does this line
appear to be a good model for the data in this scatter plot? Why or why not?
d) Use the Desmos graphing calculator (https://www.desmos.com/calculator) to construct a scatter
plot for the data given from 2010 to 2013. Label the axes of the scatter plot to reflect the
information given in the table.
i) A possible linear model for the data given from 2010 to 2013 is given by the equation
y = 0.4x + 36. Add that line to your graph of the scatter plot.
ii) Based on the equation given in part (i) predict the percent of all US college students seeking
counseling who present with depression as the main reason for counseling in the year 2018.
iii) Based on the equation given in part (i) predict the percent of all US college students seeking
counseling who present with depression as the main reason for counseling in the year 2020.
Math 037 Problem-Solving Applications (Week 5)
Page 11 of 14
e) Use the Desmos graphing calculator (https://www.desmos.com/calculator) to construct a scatter
plot for the data given from 2010 to 2012. Label the axes of the scatter plot to reflect the
information given in the table.
i) Determine the slope of the line through the data points given in 2010 and 2012. Write the
slope in decimal form, rounding to the nearest tenth if necessary.
ii) Write an equation in slope-intercept form of the line through the data points given in 2010
and 2012.
iii) Add the line with equation found in part (ii) to your graph of the scatter plot. Does this line
appear to be a good model for the data in this scatter plot? Why or why not?
f) Use the Desmos graphing calculator (https://www.desmos.com/calculator) to construct a scatter
plot for the data given from 2010 to 2012. Label the axes of the scatter plot to reflect the
information given in the table.
i) A possible linear model for the data given from 2010 to 2012 is given by the equation
y = -1x + 41. Add that line to your graph of the scatter plot.
ii) Based on the equation given in part (i) predict the percent of all US college students seeking
counseling who present with depression as the main reason for counseling in the year 2018.
iii) Based on the equation given in part (i) predict the percent of all US college students seeking
counseling who present with depression as the main reason for counseling in the year 2020.
g) Use the Desmos graphing calculator (https://www.desmos.com/calculator) to construct a scatter
plot for all of the data given from 2007 to 2013. Label the axes of the scatter plot to reflect the
information given in the table.
i) Based on the scatter plot, do the data points appear to follow a linear model, a curvilinear
model, or neither?
ii) If the data relation appears to be linear, find the slope of the line through the first and last
data points in the table (2006 and 2015) and explain the meaning of that slope in the context
of the problem.
iii) If the data relation appears to be non-linear, discuss in a few sentences some possible reasons
for the shape of the scatter plot shown.
Math 037 Problem-Solving Applications (Week 5)
Page 12 of 14
Problem 5
As a cybersecurity professional, you are always paying attention to new trends in cyberattacks. In
recent years, there has been an increase in “spear-phishing,” a form of e-mail fraud targeting a
specific organization to seek unauthorized access to confidential data.
The following table of values lists the percentage of all “spear-phishing” cyberattacks against
American businesses from 2011 – 2015 that targeted “small” businesses:
Year x
Years since 2011
y
Percentage of “spear-phishing”
cyberattacks against US businesses
targeting “small” businesses (%)
2011 0 18
2012 1 31
2013 2 30
2014 3 34
2015 4 43
(https://www.symantec.com/content/dam/symantec/docs/infographics/istr-attackers-strike-l
arge-business-en.pdf)
a) Use the Desmos graphing calculator (https://www.desmos.com/calculator) to construct a scatter
plot for the data given from 2011 to 2013. Label the axes of the scatter plot to reflect the
information given in the table.
i) Determine the slope of the line through the data points given in 2011 and 2013. Write the
slope in decimal form, rounding to the nearest tenth if necessary.
ii) Write an equation in slope-intercept form of the line through the data points given in 2011
and 2013.
iii) Add the line with equation found in part (ii) to your graph of the scatter plot. Does this line
appear to be a good model for the data in this scatter plot? Why or why not?
b) Use the Desmos graphing calculator (https://www.desmos.com/calculator) to construct a scatter
plot for the data given from 2011 to 2013. Label the axes of the scatter plot to reflect the
information given in the table.
i) A possible linear model for the data given from 2011 to 2013 is given by the equation
y = 6x + 18. Add that line to your graph of the scatter plot.
ii) Based on the equation given in part (i) what percent of all US “spear-phishing” attacks will
target small businesses in 2015?
Math 037 Problem-Solving Applications (Week 5)
Page 13 of 14
iii) Compare your answer to (ii) with the actual percent shown in the table for 2015. Is the linear
model given in part (i) a reasonable approximation over the entire period of time shown in the
table? Why or why not?
c) Use the Desmos graphing calculator (https://www.desmos.com/calculator) to construct a scatter
plot for the data given from 2012 to 2014 . Label the axes of the scatter plot to reflect the
information given in the table.
i) Determine the slope of the line through the data points given in 2012 and 2014. Write the
slope in decimal form, rounding to the nearest tenth if necessary.
ii) Write an equation in slope-intercept form of the line through the data points given in 2012
and 2014.
iii) Add the line with equation found in part (ii) to your graph of the scatter plot. Does this line
appear to be a good model for the data in this scatter plot? Why or why not?
d) Use the Desmos graphing calculator (https://www.desmos.com/calculator) to construct a scatter
plot for the data given from 2012 to 2014 . Label the axes of the scatter plot to reflect the
information given in the table.
i) A possible linear model for the data given from 2012 to 2014 is given by the equation
y = 1.5x + 29.5. Add that line to your graph of the scatter plot.
ii) Based on the equation given in part (i) what percent of all US “spear-phishing” attacks will
target small businesses in 2015?
iii) Compare your answer to (ii) with the actual percent shown in the table for 2015. Is the linear
model given in part (i) a reasonable approximation over the entire period of time shown in the
table? Why or why not?
e) Use the Desmos graphing calculator (https://www.desmos.com/calculator) to construct a scatter
plot for all of the data given from 2011 to 2015. Label the axes of the scatter plot to reflect the
information given in the table.
i) Based on the scatter plot, do the data points appear to follow a linear model, a curvilinear
model, or neither?
ii) If the data relation appears to be linear, find the slope of the line through the first and last
data points in the table (2011 and 2015) and explain the meaning of that slope in the context
of the problem.
iii) If the data relation appears to be non-linear, discuss in a few sentences some possible reasons
for the shape of the scatter plot shown.
Sample Solution
