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\centerline{MONT 102N -- Modeling the Environment}
\centerline{Midterm Exam -- October 28, 2011}
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\noindent
{\it Your Name:} $\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}$
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\noindent
{\it Directions}
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Do all work on these sheets.  You may use the back sides if necessary. 
There are 100 possible points (distributed as indicated in the questions).
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\noindent
I.  In discussing amounts of water needed for irrigation of farmland,
a common unit of volume is the acre-foot.  One acre-foot of water is
the amount of water necessary to cover a flat field one acre in area, to a depth of 
one foot.  Using the tables below, answer questions A and B.

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\item{A.} (10)  How many cubic yards (${\rm yd}^3$) of water are in one acre-foot?
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\item{B.} (10)  How many cubic meters (${\rm m}^3$) of water are in one acre-foot?
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\noindent
II.  The following table gives amounts (in tons) of materials of different types
recycled in Washington State in two years, 1986 and 1998.
$$\matrix{ {\bf Category} & {\bf 1986} & {\bf 1998}\cr
           {\rm Paper} & 391994 & 821994\cr
           {\rm Metal} & 9528 & 318710\cr
           {\rm Plastic} & 349 & 9871\cr
           {\rm Glass} & 48013 & 113338\cr
           {\rm Organics + Others} & 352 & 903466\cr}$$  
\item{A.}  (20)  Construct a pie chart for each year showing how
the total recycled materials breaks down into these categories.
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\item{B.}  (10)  Based on the pie charts, briefly describe
two differences between the two years.  
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III.   
\item{A.}  (11) In 2002, there were about $4.71 \times 10^5$ alternate
fuel vehicles (powered by electricity, ethanol, natural gas, etc.) on
the road in the U.S.  By 2004, the number had risen to $5.48 \times 10^5$.
Construct a linear model for $AFV = $ number of alternate fuel vehicles, 
as a function of $t = $ years since 2002.  What does your model predict
about the number AFV in 2011?
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\item{B.}  The following spreadsheet shows
a scatterplot for the number of AFV vehicles on the road 
(in units of $10^5$ vehicles) over a longer time period starting 
in 1995.  Mark the correct responses to the questions below.
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\noindent
1.  (3)  Based on the scatter plot, the correlation coefficient $r$ is
probably:

\leftline{ between $-1$ and $-.5$ $\underline{\qquad\qquad\qquad}$}

\leftline{ between $-.5$ and $0$ $\underline{\qquad\qquad\qquad}$} 

\leftline{ between $0$ and $.5$ $\underline{\qquad\qquad\qquad}$} 

\leftline{ between $.5$ and $1$ $\underline{\qquad\qquad\qquad}$} 
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\noindent
2.  (3) The least squares regression line for this data set would
have a slope $m$ about:

\leftline{ $m = 1/10$ $\underline{\qquad\qquad\qquad}$}

\leftline{ $m = 1/3$ $\underline{\qquad\qquad\qquad}$}

\leftline{ $m = 1$ $\underline{\qquad\qquad\qquad}$}
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\noindent
3.  (3)  Which is larger:

\leftline{ the average increase per year over the first five years $\underline{\qquad\qquad\qquad}$}

\leftline{ the average increase per year over the last five years $\underline{\qquad\qquad\qquad}$}

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\noindent
{\it Essay} (30)
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In group project 3, we studied the 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?  
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