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\centerline{MONT 100N -- Modeling the Environment}
\centerline{Midterm Exam -- October 27, 2017}
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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.  The following table gives 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.}  (15)  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.   
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II.  Burning coal provides between 9500 and 14000 BTUs of heat energy per
pound.   Using the table below, answer questions A and B.

\vglue 2.0truein

\item{A.} (5)  Express the heat energy from burning one pound of coal as a range of values
in calories.  Give the endpoints of your range in scientific notation.
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\item{B.} (5)  What is the range of heat energy values provided by burning 1 kilogram of coal, 
expressed in BTUs?
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III. (10)  The 2012 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.  If you buy the hybrid and drive about 10000 miles per year, about how many years will 
it take for your savings in gasoline costs to make up for the difference in price?  Assume that 
gasoline will average $\$ 4.00 $ per gallon over the life of your vehicle.     
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IV.   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 $5.48 \times 10^5$.
\item{A.} (5)  What was the percent change in alternate fuel vehicles from
2002 to 2004?
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\item{B.} (6)  Construct a linear model for $AFV = $ number of alternate fuel vehicles
as a function of $t = $ time in years using the information above.  Take $t = 0$ corresponding to 2002.  
What does your model predict about the number AFV in 2011?
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\item{C.}  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.  Place a check next to the correct responses to the questions below.
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1.  (3) 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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2.  (3)  Based on the scatter plot, the correlation coefficient $r$ is
probably:

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

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

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

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

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3.  (3)  Suppose you had used the two data points for 1999 and 2000 to 
construct a linear model and predicted an AFV number for 2004 from that.  
Which would be larger:

\leftline{ the actual value for AFV in 2004 $\underline{\qquad\qquad\qquad}$}

\leftline{ the predicted value for AFV in 2004 from the model $\underline{\qquad\qquad\qquad}$}

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{\it Essay} (30)
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In group project 3, we studied the flow diagram of the U.S. energy economy
in 2010 (see sheet at end of exam).  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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