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\centerline{MONT 104N -- Modeling the Environment}
\centerline{Information on Midterm Exam}
\centerline{October 16, 2012}
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\noindent
{\it General Information and Groundrules}
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As announced in class and on the revised course schedule
online, the midterm exam for our Montserrat seminar will
be given in class on Friday, October 26.  
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\item{$\bullet$} This will be a full period, individual exam.  No 
sharing of information with others 
in any form will be permitted during the exam.
\item{$\bullet$} You may use a calculator during the exam,
but {\it no other electronic devices}.
\item{$\bullet$} There will be three or four mathematical
problems (each possibly with a few separate parts).  These
questions will be similar to things you have seen on the
problem sets or the group projects.  Some sample exam questions
are given later in this document.
\item{$\bullet$}  The exam will also include an essay question 
on a set topic chosen from the topics listed below.  This part 
of the exam should take you about 15 minutes, so it will be 
necessary to spend some of your preparation time on deciding 
what you want to say for each topic.
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\noindent
{\it Possible Essay Topics}
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\item{1.}  The main discussion in Montaigne's essay {\it On Cannibals} 
concerns aspects of the culture of a group
of native people in current-day Brazil who came into contact with Europeans during 
Montaigne's lifetime. How does Montaigne describe their society? How does it compare
with European society at the time Montaigne was writing?  How does Montaigne use
the idea of the ``natural'' versus the ``artificial'' in assessing this culture? 
Would you say Montaigne expresses undiluted sympathy for and understanding of their 
customs? If not, exactly what is his attitude?
\item{2.}  In group project 3, we studied a flow diagram of the U.S. energy economy
in 2010.  Of the five end-use sectors of the economy given in that diagram,
which use energy in the {\it most wasteful} ways?  Which sectors are {\it more efficient} in 
their energy use?  Propose and discuss some likely reasons why these differences in 
efficiency exist.  Are there obvious changes that could be made to improve the efficiency 
of the most wasteful sectors?  Which of the energy sources listed in that diagram are from 
``fossil fuels'' and which are renewable resources?  Is there a clear difference in the 
efficiency of use of fossil fuels versus use of renewable resources?  
(Note: If I asked this question, I would provide a copy of the diagram for you 
to refer to.)
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\noindent
{\it Sample Mathematical Questions}
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{\it Disclaimer:}  The actual exam questions will cover the same mathematical topics and 
will be at approximately the same level of difficulty.  However the organization
and the content may be completely different.  
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\noindent
A.  (Refer to the tables on pages 6 - 8; something like those
would be supplied for your use on a question like this.)
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\item{1.}  A committee on rail freight transport recommends
increasing the mass that can be carried in a trailer
from 42 to 46 tonnes.  How much are these masses in kilograms?
In pounds?
\item{2.}  About 24 million liters of rainwater are 
discharged by a storm drain into a river.  The
concentration of toxic arsenic in the rainwater
averages 170 micrograms of arsenic per liter.
How many kilograms of arsenic are discharged into
the river each year.
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B.  In 2002, 10731 species were listed on the World
Conservation Union ``red list'' of endangered species.
In 2004, the corresponding number was 15042.
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\item{1.}  What was the ratio of the size of the 
2004 list to the size of the 2002 list?
\item{2.}  What was the percentage increase
in the size of the list from 2002 to 2004?
\item{3.}  It is not known exactly how many
species of plants and animals there are on the 
Earth today.  But say that number is estimated as
12 million. What percentage of that total number
appeared on the red list in each year?
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C.  The following table gives several African countries,
their total forest areas, and their areas of legally protected 
forests (in square kilometers)
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$$\matrix{{\rm Country} & {\rm Total} & {\rm Protected}\cr
{\rm Cameroon} & 289965 & 17845\cr
{\rm Congo} & 278979 & 12935\cr
{\rm Gabon} & 239369 & 8975\cr
{\rm Zaire} & 1439178 & 93160 \cr}$$
\item{1.}  Which country has the largest protected forest area?
\item{2.}  Which country has the largest percentage of protected forest?
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D.  A cubic meter of air has a mass of about 1.25 kg.  About 2 mg of
that mass is methane.  What is the mass concentration of methane in 
air, expressed in parts per million?
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E.  The US EPA Toxic Release Inventory for 2000 includes the 
following information:
$$\matrix{{\rm State} & {\rm Toxics\ (in\ 10^6 lb)}\cr
{\rm Nevada} & 1000\cr
{\rm Utah} & 956 \cr
{\rm Arizona} & 744\cr
{\rm Alaska} & 535 \cr
{\rm Texas} & 302 \cr}$$
\item{1.}  Construct a bar chart showing this information.  Label your vertical axis.
\item{2.}  Construct  pie chart showing the portions of the 
total toxics from these five states that each state contributes.
\item{3.}  Which state or states is approximately ``twice as
toxic'' as Alaska.
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F.  Look at the plot in Figure 3-28 on page 71 of the text, which 
shows the gray wolf population in Wisconsin from 1980 to 2002.
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\item{1.}  Note that the portion of the graph representing
the years 1980 to 1992 looks quite linear.  Estimate
a linear model for this period by using the line
through the two points $(1980,50)$ and $(1990,60)$.  (Determine
the equation of the line through those points.)
\item{2.}  Do the same for the period 1993-2002
using the two points $(1993,70)$ and $(2002,325)$.
\item{3.}  What are the slopes of these two lines?  What are the 
units of the slope and what do they represent in real world
terms?
\item{4.}  Look at the spreadsheet link from the course homepage
accompanying this review sheet.  The plot shows the 
least squares regression line for the whole data set, 
together with the computed slope and intercept values
for the regression line.  
Which method seems superior in this case -- using two
different lines for different time periods, or one 
regression line for the whole time?  Explain how 
you are making this decision.
\bye
