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\centerline{MONT 104N -- Modeling the Environment}
\centerline{Information on Midterm Exam}
\centerline{October 23, 2019}
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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, November 1.  
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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 first three
problem sets (material up to and including the discussion of exponential models from
Chapter 5) and the group projects from Chapters 1 - 3
of our text.  Some sample exam questions
are given later in this document.
\item{$\bullet$}  The exam will also include an essay question 
on a set topic given below.  As you will see, part of this consists of 
several factual questions.  {\it You will need to look up some information
before coming to the exam to write this part of the essay.  Online 
sources will be the best way to gather this information.}  
Then, the rest of the essay topic asks you to take a stand one way or 
another on the issues raised.  
There's no one right or wrong answer for that part; the point 
is to get you to think about the issues and try to 
formulate a position of your own.   This section 
of the exam should take you about 15 minutes or so, so it will be 
necessary to spend some of your preparation time on deciding 
what you want to say.
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\noindent
{\it Essay Prompt}
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There is an ongoing movement at this point in history (i.e. 2019) 
that is especially strong in Sweden, where it known as {\it flygskam}.  
What does this Swedish word mean in English?  What actions 
are proponents of {\it flygskam} urging other people not to continue
doing, and what are their reasons for doing this?  Part of the underlying reason
for the existence of this movement is concern about how the actions are 
influencing greenhouse gas levels in the atmosphere.   What proportion of
current $CO_2$ emissions can be attributed to these actions and which people
are contributing most to this? 
While the recommendations of proponents of {\it flygskam} might make
a lot of sense from the environmental point of view, there are also 
certainly aspects of modern life that would be drastically changed if those
recommendations were adopted by everyone.  [Note:  The opinion part starts here.]  
What would we be losing by following those recommendations?  Are the
environmental benefits great enough to justify the 
costs to individuals and society of adopting those recommendations? 
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{\it Something to think about in conjunction with this essay topic}
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{\it Travel is fatal to prejudice, bigotry, and narrow-mindedness, 
and many of our people need it sorely on these accounts. Broad, 
wholesome, charitable views of men and things cannot be acquired 
by vegetating in one little corner of the earth all one's lifetime.}  
Mark Twain (1835-1910)
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\noindent
{\it Sample Mathematical Questions}
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\noindent
{\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
I.  The following table gives estimates of the amounts of carbon (in units of $10^{15}$ kilograms)
contained in the major ``reservoirs'' of this element on planet Earth:
$$\matrix{ {\bf Reservoir} & {\bf Carbon\ Content }\cr
           {\rm Atmosphere} & .59 \cr
           {\rm Crust\ (as\ fossil\ fuels)} & 3.7 \cr
           {\rm Vegetation} & 2.3 \cr
           {\rm Shallow\ Ocean} & .9  \cr
           {\rm Deep\ Ocean} & 37.3\cr}$$ 
\item{A.}  What percent of the total carbon present on 
Earth is contained in each of these reservoirs?
$$\matrix{ {\bf Reservoir} & {\bf Percent\ of\ Total\ Carbon}\cr
& \cr
           {\rm Atmosphere} & \underline{\qquad\qquad\qquad\qquad}\cr
&\cr
           {\rm Crust\ (as\ fossil\ fuels)} & \underline{\qquad\qquad\qquad\qquad}\cr
&\cr
           {\rm Vegetation} & \underline{\qquad\qquad\qquad\qquad} \cr
&\cr
           {\rm Shallow\ Ocean} &  \underline{\qquad\qquad\qquad\qquad}\cr
&\cr
           {\rm Deep\ Ocean} & \underline{\qquad\qquad\qquad\qquad} \cr}$$  

\item{B.}  Construct and draw a chart (your choice of type) showing how
the total carbon breaks down into these categories.  
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\noindent
II.  Burning coal provides between 9500 and 14000 BTUs of heat energy per
pound.  Using the information below, answer questions A and B:
\item{$\bullet$}  $1\ {\rm lb} \doteq .454\ {\rm kg}$
\item{$\bullet$}  $1\ {\rm BTU} \doteq .252\ {\rm Kilocalorie}$
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\item{A.} Express the heat energy from burning one pound of coal as a range of values
in Kilocalories.  Give the endpoints of your range in scientific notation.
\item{B.}  What is the range of heat energy values provided by burning 1 kilogram of coal, 
expressed in BTUs?
\item{C.} If the 9500 BTU figure comes from bituminous coal and the 14000 BTU comes
from anthracite coal, what is the percentage difference in heat energy between anthracite and bituminous?  
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\noindent
III. The Honda Civic comes in a standard (gasoline engine) version and a 
hybrid (gasoline-electric) version.  The standard version has a fuel efficiency of about 34 miles per 
gallon, while the hybrid version gets about 44 miles per gallon.  
The hybrid version has a ``sticker price'' (that is, the nominal cost to buy the car new) about 
$\$ 4000$ more than the standard.  You drive about 10000 miles per year.
Assume that gasoline will average $\$ 3.00 $ per gallon over the life of your vehicle.    
\item{A.}  How many gallons of gasoline would you use to drive the 10000 miles with each version?
\item{B.}  What is the difference between your costs for gasoline with the two versions?
\item{C.}  If you bought the hybrid version, about 
how many years would it take for your savings in gasoline costs to make up for the difference in 
sticker price?  
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\noindent
IV.  The link next to the one where you downloaded this review sheet shows a spreadsheet scatter plot.
Place a check next to the best responses to the questions below.
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\item{A.}  (5) The least squares regression line for this data set would
have a slope $m$ about:

\leftline{ $m = -.1$ $\underline{\qquad\qquad\qquad}$}

\leftline{ $m = .3$ $\underline{\qquad\qquad\qquad}$}

\leftline{ $m = 1$ $\underline{\qquad\qquad\qquad}$}
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\noindent
B.  (5)  Based on the scatter plot, the $R^2$ statistic is
probably:

\leftline{ between $.8$ and $1$ $\underline{\qquad\qquad\qquad}$} 

\leftline{ between $.4$ and $.6$ $\underline{\qquad\qquad\qquad}$} 

\leftline{ between $.2$ and $.4$ $\underline{\qquad\qquad\qquad}$} 

\leftline{ between $.0$ and $.2$ $\underline{\qquad\qquad\qquad}$}

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V.  Wind power has emerged as one of the faster-growing methods
of electricity generation in recent years.  In 2016, the generating power 
of wind turbines installed around the world was about
$301$ gigawatts and it was increasing at about $33.2\%$ per
year.
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\item{A.} The typical English unit of power is the horsepower.
$1 {\rm\ horsepower} = 7.457 \times 10^{-7}$ gigawatts.  Convert $301$ gigawatts
to the equivalent number of horsepower.
\item{B.} Construct an exponential model for $WP = $
wind power generation as a function of
$t = $ years after 2016.  {\it Use units of $10^2$ gigawatts for WP} -- see
the entry for 2016 in the table below.
\item{C.}  Compute the values of $WP$ predicted by
your model for the years $2017 - 2022$.   Round to 2 decimal places.
About how many years will it take for $WP$ to reach approximately 
double the 2016 level?
\item{D.} How many years will it take for wind power generation
to reach $2.0 \times 10^3$ gigawatts according to your model?
\bye
