Week 13 – Mathematical ModelingGraded Assignment – Developing and Interpreting
Exponential Models
In Exercises 1–4 round answers to 2 decimal places. (Maximum 25 points each)
1. “Charlie’s Birdhouses has an annual growth rate 10%. If Charlie made
120 birdhouses in 2010, how many birdhouses will he make in 2015?
2. Karen has large Christmas party each year for family and friends. In
1990 there were 12 guests, but the number of attendees has increased by
5% every-other-year since. How many people should she expect for her
2012 Christmas party?
3. When mining and refining Uranium 238 for use in nuclear reactors, one
of the byproducts is 243Th, which has a half-life of approximately 24
days. If there were originally 24.5 g of the isotope on January 1, 2011,
how much will remain on December 31, 2011?
4. The human body produces an enzyme, ornithice decarboxylase that has
a half-life of approximately 11 minutes. If 131 mg are present, how
much will be left in 1 hour?
Adapted with permission
Gallo, Harvey, & Clark, © 2011
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Week 12 – Mathematical Modeling
Discussion Question – Interpreting Exponential Models
Review the information about exponential growth in air traffic on page 14 of the
IATA report provided by the following link:
https://www.iata.org/policy/Documents/aviation-benefits-%20web.pdf
Answer the questions below.
1. Using the information provided in the article, make a prediction for airlines worldwide
Revenue-Passenger-Kilometers in the years 2031 and 2046. Discuss how you arrived at
your predictions and what factors you believe support your prediction.
2. Using the information provided in the article, make a prediction for airlines worldwide
Freight-Tonne-Kilometers in the years 2026 and 2036. Discuss how you arrived at your
predictions and what factors you believe support your prediction.
Adapted with permission
Gallo, Harvey, & Clark, © 2011
Page | 1
Week 10 – Probability
Graded Assignment – Calculating and Interpreting Relative
Risk
In Exercises 1–4, interpret the given findings in the context of relative risk as in Example 8.
(Maximum 25 points each)
1. The contingency table below contains fictitious data that reflect the results of a medical
study designed to assess the effectiveness of a new drug on reducing deaths. Based on
these data determine and interpret the relative risk of a patient dying with respect to the
two treatments.
Type of Treatment
New drug
Placebo
Patient Lived
135
144
Patient Died
15
36
2. The contingency table below contains fictitious data that reflect the results of a highway
safety study designed to assess the habits of automobile drivers. Based on these data
determine and interpret the relative risk of a driver using a cell phone while driving for
people under the age of 50 and those 50 or older.
Age
Under 50
50 or older
Adapted with permission
Gallo, Harvey, & Clark, © 2011
Uses Cell Phone Doesn’t Use Cell Phone
240
15
30
210
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3.
The contingency table below contains fictitious data that reflect the results of an
epidemiology study designed to assess effectiveness of a flu vaccine. Based on these data
determine and interpret the relative risk of a person developing the flu who was vaccinated
versus a person who was not vaccinated.
Type of Treatment
Flu vaccine
No vaccine
4.
Person Got Flu
12
45
Person Did Not Get Flu
88
85
The contingency table below contains fictitious data that reflect the results of a survey
conducted by a Part 61 flight school designed to assess the differences between males and
females with respect to their tendency to drop out of flight school. Based on these data
determine and interpret the relative risk of females dropping out of flight school compared
to males.
Gender
Male
Female
Adapted with permission
Gallo, Harvey, & Clark, © 2011
High Tendency
75
120
Low Tendency
125
80
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