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\leftline{Mathematics 133 -- Intensive Calculus for Science 1}
\leftline{Makeup Exam I -- October 4, 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: $f(x),g(x),h(x)$.  
$$\matrix{x  &0 &1 &2 &3 &4 \cr
       f(x)  &0 &1.5 &3.0 &4.5 &6.0 \cr
       g(x)  &3 &12 &24 &48 &96 \cr
       h(x)  &3.7 &3.4 &3.1 &2.8 &2.5 \cr}$$
\item{A)}  (10) Which (if any) of these are linear functions?  
For those that are linear give formula(s).
\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)  This year's Nobel Prize in Medicine went to two Australian 
researchers who showed that bacteria called {\it Helicobacter pylori}
actually cause most stomach ulcers in humans (not excess stomach acid
as most people thought before).  A colony of {\it Helicobacter pylori} 
in a certain math prof's stomach is growing at a continuous rate of 
$0.1 \%$ per month.  How long will it take for the colony to {\it double} 
in size?  (When it doubles, he gets an ulcer.)
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III. The back of this sheet shows the graph of a polynomial
function $f(x)$. 
\item{A)} (15) Find a possible formula for $f(x)$.  
\item{B)} (10) Does $f(x)$ have an inverse function?  Why or 
why not?
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IV. (20)  The average depth of the water in a bay is 20ft.
Because of tides, the depth varies sinusoidally
with amplitude 5ft.  The period is 12.5 hours.  Give a 
possible formula for the depth as a function of $t$ (in hours).
Say what the height is at $t = 0$ using your formula.
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V.  All parts of this question refer to the rational function 
$$r(x) = {x^2-6x+8\over 3x^2-3}.$$
\item{A)} (5) Where does the graph of $r(x)$
have vertical asymptotes?  
\item{B)} (5) Where does the graph of $r(x)$ cross the $x$-axis?
\item{C)} (5) Where does the graph have a horizontal asymptote?  
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