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\leftline{Mathematics 133 -- Intensive Calculus for Science 1}
\leftline{Exam I -- September 28, 2005}
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{\it Directions}:  Do all work in the blue exam booklet. 
There are 100 possible points, distributed as indicated before
the questions -- (10) means the question is worth 10 points
for instance.  No calculators on this exam.
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I.  The following table contains values for
three different functions: $f(x),g(x),h(x)$.  
$$\matrix{x  &-2 &0  &2 &4 &6\cr
       f(x)  & 1 & 0 & 3 & 2 & 1 \cr
       g(x)  &23 &28 &33 &38 &43 \cr
       h(x)  &18 &2 &2/9 &2/81 &2/729 \cr}$$
\item{A)}  (10) Which (if any) of these are linear functions?  
For those that are linear give a formula.
\item{B)}  (10) Which (if any) of these are exponential functions?  
For those that are exponential, give a formula.
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II.  (20) The radioactive element Explosium${}^{224}$ decays exponentially
with a half-life of 12 years.  If 10 g are present originally 
in a sample, how long will it take for the amount to decay to 1 g?
(Leave your answer in ``exact form''.)
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III. (30) The back of this sheet shows two plots A and B. 
Find possible formulas for the two functions
and explain how you determined your results.
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IV. (15) Does the function $f(x) = 10^{x + 1}$ have an 
inverse function?  If so, say why and find a formula for
the inverse function.  If not, say why not.
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V.  (15) All parts of this question refer to the rational function 
$$r(x) = {2x^2 - x\over 16 - x^2}.$$
\item{A)} (5) Where does the graph of $r(x)$
have vertical asymptotes?  
\item{B)} (5) Where does the graph have a horizontal asymptote?  
\item{C)} (5) Where does the graph of $r(x)$ cross the $x$-axis?
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