The Table Below Shows the Number of Licensed Hotels with at Least

question 29

Essay

The table below shows the number of licensed hotels with at least 15 rooms in New South Wales from March 1998 to December 2009. $\quad$
$\begin{array}{ll}\text { Mar-1998 } & 175 \\\text { Jun-1998 } & 174 \\\text { Sep-1998 } & 174 \\\text { Dec-1998 } & 172 \\\text { Mar-1999 } & 177 \\\text { Jun-1999 } & 171 \\\text { Sep-1999 } & 176 \\\text { Dec-1999 } & 179 \\\text { Mar-2000 } & 181\\\text { Jun-2000 } & 184 \\\text { Sep-2000 } & 191 \\\text { Dec-2000 } & 194 \\\text { Mar-2001 } & 198 \\\text { Jun-2001 } & 198 \\\text { Sep-2001 } & 199 \\\text { Dec-2001 } & 201 \\\text { Mar-2002 } & 198 \\\text { Jun-2002 } & 196 \\\text { Sep-2002 } & 195 \\\text { Dec-2002 } & 198 \\\text { Mar-2003 } & 199 \\\text { Jun-2003 } & 202 \\\text { Sep-2003 } & 201 \\\text { Dec-2003 } & 201\\\text { Mar-2004 } & 199 \\\text { Jun-2004 } & 199 \\\text { Sep-2004 } & 198 \\\text { Dec-2004 } & 197 \\\text { Mar-2005 } & 199 \\\text { Jun-2005 } & 199 \\\text { Sep-2005 } & 198 \\\text { Dec-2005 } & 199 \\\text { Mar-2006 } & 202 \\\text { Jun-2006 } & 205 \\\text { Sep-2006 } & 203 \\\text { Dec-2006 } & 201\\\text { Mar-2007 } & 202 \\\text { Jun-2007 } & 200 \\\text { Sep-2007 } & 202 \\\text { Dec-2007 } & 202 \\\text { Mar-2008 } & 201 \\\text { Jun-2008 } & 203 \\\text { Sep-2008 } & 204 \\\text { Dec-2008 } & 203 \\\text { Mar-2009 } & 203 \\\text { Jun-2009 } & 206 \\\text { Sep-2009 } & 203 \\\text { Dec-2009 } & 210\end{array}$ a. Plot the time series.
b. When did the number of licensed hotels with at least 15 rooms in New South Wales grow fastest?

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Definitions:

\(34\)

An integer and natural number following 33 and preceding 35.

\(k ^ { 3 }\)

Represents the cube of a variable \(k\), equivalent to multiplying \(k\) by itself twice (\(k*k*k\)).

\(k + 8\)

An algebraic expression representing the sum of a variable, \(k\), and the number 8.