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\leftline{Mathematics 133 -- Intensive Calculus for Science 1}
\leftline{Sample Exam I -- September 21, 2001}
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{\it Directions :}  Do all work in the blue exam booklet.  You
may use a calculator on any of the following problems.  There are
100 possible points, distributed as indicated.
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I.  The following table contains values for
three different functions: $f(x),g(x),h(x)$.  
$$\matrix{x = &-2 &0  &2 &4 &6\cr
       f(x) = & -2.1& 0 & 3.4 & 2.3 & 1.1 \cr
       g(x) = &23.1 &25.3 &27.5 &29.7 &31.9\cr
       h(x) = &10.67 & 26.67 & 66.67 & 166.67 & 416.67 \cr}$$
\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 (approximately)
exponential functions?  For those that are approximately exponential, 
give a formula.
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II.  (20) A radioactive element has a half-life of 12 years.  If 10 oz.
are present originally in a sample, how long will it take for the amount to 
decay to 1 oz.?
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III.  (15) The following graph shows $y = f(x)$.  Copy this graph in 
your exam booklet, and on the same axes, sketch $y = 3f(x + 1) - 1$.
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IV. (15) Solve for $x$:  $e^{-5x} = 10^{x + 2}$.
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V. (15) Find a possible formula for the following function.
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VI. (15) Suppose that $Q(t)$ with domain $0 \le t < 24$ (time in hours)
is the temperature in Worcester as a function of time on a typical day 
in September.  Would you expect $Q$ to have an inverse function?
If so, say what the equation $Q^{-1}(65) = 11$ means.  If not, say why not.
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