Problem 1
You are interested in building a pool in your backyard. Before selecting a pool size, you want to know
how much space it will require and how much it will cost to fill with water. Rectangular pools are
typically twice as long on one side as the other and have an average depth of 5.5 feet. You have decided
that you want your pool to have an even depth.
You consulted with a pool builder and learned that these are the three “standard” sizes for rectangular
pools (Note: All measurements are in feet):
Pool Size Width (ft) Length (ft) Depth (ft)
Small 10 20 5.5
Medium 15 30 5.5
Large 20 40 5.5
Part I: Determining Surface Area
The formula for determining the surface area is: Surface Area = Width x Length.
a. You would like to determine if the small pool would fit in your backyard, so you need to find the
surface area of the small pool. What is the surface area of the small pool? Write a complete
answer, including appropriate units.
b. You would like to determine if the medium pool would fit in your backyard, so you need to find
the surface area of the medium pool. What is the surface area of the medium pool? Write a
complete answer, including appropriate units.
c. You would like to determine if the large pool would fit in your backyard, so you need to find the
surface area of the large pool. What is the surface area of the large pool? Write a complete
answer, including appropriate units.
Part II: Determining Volume
The formula for determining volume is: Volume = Width x Length x Depth
d. What is the volume of the small pool? Write a complete answer, including appropriate units.
e. What is the volume of the medium pool? Write a complete answer, including appropriate units.
f. What is the volume of the large pool? Write a complete answer, including appropriate units.
Math 037 Problem-Solving Applications (Week 1)
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Problem 2
Your business is planning an advertising campaign in the Mid-Atlantic States. This region often includes
New York, New Jersey, Pennsylvania, Delaware, Maryland, Washington, D.C., Virginia, and West Virginia.
Since the marketing budget is tight, it is important to get an understanding of the size of the population
in each of these States, in order to properly apportion the resources.
The population estimates for the 8 states and District of Columbia are listed in the table below:
(http://factfinder.census.gov/faces/tableservices/jsf/pages/productview.xhtml?pid=PEP_2015_PEPANN
RES&src=pt)
Population Estimate (as of July 1)
State 2010 2015
New York 19,402,920 19,795,791
New Jersey 8,803,881 8,958,013
Pennsylvania 12,712,014 12,802,503
Delaware 899,791 945,934
Maryland 5,788,409 6,006,401
Washington, D.C. 605,126 672,228
Virginia 8,025,787 8,382,993
West Virginia 1,854,225 1,844,128
Part I: Population Estimates
a. What is the total population estimate for the Mid-Atlantic States as of July 1, 2015?
b. What is the total population estimate for the Mid-Atlantic States as of July 1, 2015? Round your
answer to the nearest thousand.
c. What is the total population estimate for the Mid-Atlantic States as of July 1, 2015? Round your
answer to the nearest million.
Part II: Relative Change in Population
The relative change in population since 2010 is defined as:
d. What is the relative change in population between 2010 and 2015 for West Virginia? Express
your answer in decimal format, rounded to the nearest thousandth.
e. What is the relative change in population between 2010 and 2015 for Maryland? Express your
answer in decimal format, rounded to the nearest thousandth.
f. What is the relative change in population between 2010 and 2015 for New York? Express your
answer in decimal format, rounded to the nearest thousandth.
Math 037 Problem-Solving Applications (Week 1)
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Problem 3
You are a financial planner, who helps people plan for important life events, including vacations,
weddings, and retirement. As part of the financial planning process, you have clients compare their
spending habits to that of the average American consumer.
The following table contains information from the 2013 Consumer Expenditure Survey, regarding the
fraction of consumer spending spent on different expenditures:
(http://www.bls.gov/opub/btn/volume-4/consumer-expenditures-vary-by-age.htm)
Total Expenditures Fraction of Spending
Food
Housing
Clothing
Transportation
Healthcare
Entertainment
Pensions and Social Security
Other
a. What fraction of spending goes for the combination of food and housing?
b. What fraction of spending goes for the combination of entertainment and “other”
expenditures?
c. What fraction of spending goes for transportation and healthcare?
d. Suppose a client spends a total of $58,000 on the expenditures listed in the table. How much
would the client be spending on pension and social security?
e. Suppose a client spends a total of $72,000 on the expenditures listed in the table. How much
would the client be spending on clothing?
f. Suppose a client spends a total of $64,000 on the expenditures listed in the table. How much
would the client be spending on housing?
Math 037 Problem-Solving Applications (Week 1)
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Problem 4
You work for an organization that provides mental and physical health care services across the lifespan.
The organization is currently assessing the projected demand for mental and physical health care
services over the next 20 years. As part of this process, you are tasked with determining the fraction of
the population that falls into different age groups.
The U.S. population estimates by age groups as of July 1, 2010 and 2015 are listed in the table below:
(http://factfinder.census.gov/faces/tableservices/jsf/pages/productview.xhtml?src=bkmk)
Population Estimate (as of July 1)
Age 2010 2015
Under 18 years 74,123,035 73,645,111
18 to 64 years 194,744,535 200,012,857
65 years and over 40,479,293 47,760,852
85 years and over 5,542,810 6,287,161
Total 309,346,863 321,418,820
a. What is the total U.S. population estimate as of July 1, 2015? Round your answer to the nearest
thousand.
b. What is the total U.S. population estimate as of July 1, 2015? Round your answer to the nearest
million.
c. What is the population estimate for age of under 18 years as of July 1, 2010? Round your answer
to the nearest thousand.
d. What is the population estimate for age of under 18 years as of July 1, 2015? Round your answer
to the nearest million.
e. What is the population estimate for the age group between 18 and 64 years as of July 1, 2010?
Round your answer to the nearest thousand.
f. What is the population estimate for the age group between 18 and 64 years as of July 1, 2015?
Round your answer to the nearest million.
g. What is the population estimate for age of 65 years and over as of July 1, 2015? Round your
answer to the nearest thousand.
h. What is the population estimate for age of 65 years and over as of July 1, 2015? Round your
answer to the nearest million.
i. What is the population estimate for age of 85 years and over as of July 1, 2010? Round your
answer to the nearest thousand.
j. What is the population estimate for age of 85 years and over as of July 1, 2015? Round your
answer to the nearest million.
Math 037 Problem-Solving Applications (Week 1)
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Problem 5
You are an environmental management expert at a disaster preparedness organization; your
organization prepares for a variety of natural disasters, including tsunamis. Tsunamis are ocean waves
that occur, when there has been a sudden displacement water as a result of natural occurrences such as
earthquakes or volcanic activity. As part of preparedness management, you need to have an
understanding of how fast a tsunami can travel as this affects warning systems.
The velocity(v) of a Tsunami, in kilometers per hour, can be modeled by the following formula:
where D is the depth of the water measured in meters.
a) If the depth D is 5000 meters, what is the velocity of the tsunami in kilometers per hour. Round
your answer to the nearest hundredth.
b) If the depth D is 4000 meters, what is the velocity of the tsunami in kilometers per hour. Round
your answer to the nearest hundredth.
c) If the depth D is 3000 meters, what is the velocity of the tsunami in kilometers per hour. Round
your answer to the nearest hundredth.
d) If the depth D is 2000 meters, what is the velocity of the tsunami in kilometers per hour. Round
your answer to the nearest hundredth.
e) If the depth D is 1000 meters, what is the velocity of the tsunami in kilometers per hour. Round
your answer to the nearest hundredth.
f) If the depth D is 500 meters, what is the velocity of the tsunami in kilometers per hour. Round
your answer to the nearest hundredth.
g) If the depth D is 300 meters, what is the velocity of the tsunami in kilometers per hour. Round
your answer to the nearest hundredth.
Math 037 Problem-Solving Applications (Week 1)
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Problem 6
As a scientist working for NASA, you have been looking for planets that might support extraterrestrial
life. As part of research team, you are exploring the existence of exoplanets; exoplanets are planets that
orbit stars other than our sun. As of September, 2016, NASA has listed 3,394 confirmed exoplanets
(https://exoplanets.nasa.gov/newworldsatlas/ ). Of particular interest are the “terrestrial” exoplanets;
that is, planets that are less than twice the size of Earth and orbit their stars in the conservative
habitable zone—the range of distances where liquid water could pool on the surface of an orbiting
planet.
Below is a list of 10 “terrestrial” exoplanets identified by NASA:
Host Star Planet Letter Distance from Earth (light years) Discovery Year
PSR B1257+12 b 1957 1994
GJ 667 C e 22 2013
Trappist-1 c 39 2016
HD 20794 b 20 2011
GJ 3998 b 58 2016
K2-19 d 949 2016
Keppler-1542 d 1096 2016
GJ 1132 b 39 2015
Proxima Cen b 4 2016
KOI-55 b 3849 2011
Part I: Converting Light Year Distances to Miles
A light-year is the distance light travels in one year, roughly 5.879×1012 miles.
For example: What is the distance in miles from Earth to Keppler-1542 d? To answer this question, we
multiply the light year distance by 5.879×1012 miles.
1096 light years * 5.879×1012 miles/lightyear ≈ 6.443×1015 miles.
a. About how far is Proxima Cen b from the Earth in miles? Write your answer in scientific notation and
include appropriate units.
b. About how far is KOI-55 b from the Earth in miles? Write your answer in scientific notation and
include appropriate units.
Part II: Space Travel
c. Exoplanet HD 20794 b is about 1.7637×1014 miles from Earth. The fastest spacecraft to leave Earth, so
far, New Horizons, is currently traveling out of the solar system at about 32,000 miles per hour. At that
rate, how long would it take, in hours, for a spacecraft to travel from Earth to exoplanet HD 20794 b?
Write your answer in scientific notation and include appropriate units.
Math 037 Problem-Solving Applications (Week 1)
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d. Exoplanet K2-19 d is about 5.579×1015 miles from Earth. The fastest spacecraft to leave Earth, so far,
New Horizons, is currently traveling out of the solar system at about 32,000 miles per hour. At that rate,
how long would it take, in hours, for a spacecraft to travel from Earth to exoplanet K2-19 d? Write your
answer in scientific notation and include appropriate units.
Part III: Star Trek and Warp Speed
In the original Star Trek series, the Enterprise traveled at speeds measured by “warp factors.”
A warp factor of 1 was equal to the speed of light, 6.706×108 mph.
To find the speed of a higher warp factor, multiply the speed of light by the cube of the warp
factor. For example, at warp 4, the speed is 43
times the speed of light, or 43
×6.706×108 mph.
e. Exoplanet Kepler-1542 d is about 6.443×1015 miles from Earth. If the Enterprise traveled at warp 4
from Earth to Kepler-1542 d, how long would the journey take? Write your answer in scientific notation
and include appropriate units.
f. Exoplanet Kepler-1542 d is about 6.443×1015 miles from Earth. If the Enterprise traveled at warp 9
from Earth to Kepler-1542 d, how long would the journey take? Write your answer in scientific notation
and include appropriate units.
Sample Solution
