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\noindent {\bf Problem statement} Below is the U.S.~inflation rate for
the months of June through December in the year 1920. This rate is
``an annualized percentage rate of change of the U.S.~consumer price
index (CPI) as measured by price changes for the month cited.''





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\settabs 7\columns
 \+\quad\ \thinspace June & \ \thinspace July & August & September & October & November & December\cr
\+\quad 23.67\% & 19.54\% &  14.69\% &  \ \ 12.36\% &  \ \ 9.94\% & \
 \ \thinspace
  7.03\% &
\ \ \thinspace 2.65\%\cr
}


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\noindent The data points given are displayed on the graph to the
right.  Suppose $C(t)$ is the U.S.~CPI for the months listed, and $t$
represents the month of the year (so $t=6$ represents June).  Use the
numbers to answer the following questions as well as you can.  

\medskip

\noindent a) What is the sign of $C'(t)$ for $t$ in the interval
$[6,12]$?

\medskip

\noindent b) What is the sign of $C''(t)$ for $t$ in the interval
$[6,12]$?

\medskip

\noindent c) Describe in one or more English sentences what is
happening to} 

\noindent the CPI in the interval $[6,12]$ as completely as
possible. (Your description could begin, ``Princes are $\ldots$'' but
include all relevant qualitative information in your description.)

\medskip

\noindent d) Sketch a qualitatively correct graph of the function
$C(t)$ in the interval $[6,12]$.

\vfil\eject\end

1.~What is the sign of $C'(t)$ for $t$ in the interval $[6,12]$?

\noindent {\bf Answer} Remember that the rates quoted represent the {\it
changes}\/ in CPI. Since all of the changes shown are positive, I
think that $C'(t)>0$ for $t$ in $[6,12]$.

\smallskip

2.~What is the sign of $C''(t)$ for $t$ in the interval $[6,12]$?

{\bf Answer} Since the numbers shown are {\it decreasing}, and the
numbers themselves are rates of change (sort of -- so they are almost
$C'(t)$ numbers) I think that $C''(t)<0$ for $t$ in the interval
$[6,12]$.

\smallskip

3.~Describe in English what is happening to the CPI in the interval  $[6,12]$??

{\bf Answer} Prices increase throughout the time interval considered,
but the rate of increase is slowing.

\smallskip

4.~
