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\textbf{College of the Holy Cross, Fall Semester 2017} \\
\textbf{MONT 100N -- Modeling the Environment} \\
\textbf{Midterm Exam, October 27}

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\noindent\textbf{Your Name}: \underline{\phantom{Name Name Name Name Name}}

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\paragraph{Instructions} Please write your answers in the spaces
provided on the following pages, and show work on the test itself. \textbf{For possible
partial 
credit, you must show work}. Use the back of the preceding
page if you need 
more space for scratch work.



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\noindent\textbf{Please do not write in the space below}


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\begin{tabular}{|l||r|}

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Problem & Points/Poss    \strut \\

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I  & \hfil/\  25\hfil \strut \\

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II  & \hfil/\  20\hfil \strut \\

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III  & \hfil/\  15\hfil \strut \\

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IV  & \hfil/\  10\hfil \strut \\

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Essay  & \hfil/\  30\hfil \strut \\


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Total   & \hfil/100\hfil \strut \\

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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:
$$\matrix{ {\bf Reservoir} & {\bf Carbon\ Content }\cr
           {\rm Atmosphere} & .59 \cr
           {\rm Crust\ (as\ fossil\ fuels)} & 3.7 \cr
           {\rm Vegetation} & 2.3 \cr
           {\rm Shallow\ Ocean} & .9  \cr
           {\rm Deep\ Ocean} & 37.3\cr}$$ 
\begin{enumerate} 
\item[A.]  (10)  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.]  (15)  Construct and draw a chart (your choice of type) showing how
the total carbon breaks down into these categories.  
\end{enumerate} 
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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:
\begin{itemize}
\item  $1\ {\rm lb} \doteq .454\ {\rm kg}$
\item  $1\ {\rm BTU} \doteq .252\ {\rm Kilocalorie}$
\end{itemize}
\vglue 10pt 
\begin{enumerate}
\item[A.] (8)  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.
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\item[B.] (8)  What is the range of heat energy values provided by burning 1 kilogram of coal, 
expressed in BTUs?
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\item[C.] (4) 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?  
\end{enumerate}
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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 price 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.    
\begin{enumerate}
\item[A.]  (5)  How many gallons of gasoline would you use to drive the 10000 miles with each version?
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\item[B.]  (5)  What is the difference between your costs for gasoline with the two versions?
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\item[C.]  (5)  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 price?  
\end{enumerate}
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\noindent
IV.  Consider the Excel scatter plot below.
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Place a check next to the best responses to the questions below.
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\noindent
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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\noindent
{\it Essay} (30)
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In \S 193 of the {\it Laudato Si'} encyclical letter, Pope Francis seems to suggest that
economic growth should be be contained or reversed
 in order to achieve ``sustainable development.''  But economic growth in the developing 
world has lifted millions into the ``global middle class'' in recent decades and there
is strong sentiment in countries like India that they {\it deserve} to experience
the benefits of economic development like the development that has occurred in North America
and Europe.  Do more developed countries have the right to say ``no'' to those desires?  
Francis suggests redefining what we mean by ``progress'' to address these questions (\S 194), 
but is that realistic or desirable?  
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