document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192979>Question 1192979</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Topics In Contemporary Math<BR>\n" );
document.write( "    Linear Growth\r<BR>\n" );
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document.write( "4) The average amount a television viewer spent on merchandise, apparel, and snacks when <BR>\n" );
document.write( "watching a Super Bowl game is shown. <BR>\n" );
document.write( "Year 2005 2007 2009 2011 2012<BR>\n" );
document.write( "Amount $38.35 $56.04 $57.27 $59.33 $63.87\r<BR>\n" );
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document.write( "a) If we consider 2005 as the base year, write an explicit formula for 𝑃𝑛, the amount of <BR>\n" );
document.write( "money spent on merchandise, apparel, and snacks when watching a Super Bowl game for <BR>\n" );
document.write( "n years after 2005.\r<BR>\n" );
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document.write( "b) How much would the model predict is spent in 2022?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848944 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=848944\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **a) Find the Explicit Formula**\r<BR>\n" );
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document.write( "1. **Calculate the Average Annual Increase:**\r<BR>\n" );
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document.write( "   * Find the differences in spending between consecutive years:<BR>\n" );
document.write( "      * 2007 - 2005: $56.04 - $38.35 = $17.69<BR>\n" );
document.write( "      * 2009 - 2007: $57.27 - $56.04 = $1.23<BR>\n" );
document.write( "      * 2011 - 2009: $59.33 - $57.27 = $2.06<BR>\n" );
document.write( "      * 2012 - 2011: $63.87 - $59.33 = $4.54\r<BR>\n" );
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document.write( "   * Calculate the average annual increase:<BR>\n" );
document.write( "      * (17.69 + 1.23 + 2.06 + 4.54) / 4 = $6.38\r<BR>\n" );
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document.write( "2. **Write the Explicit Formula:**\r<BR>\n" );
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document.write( "   * Since we're assuming linear growth, the formula for the amount spent (Pn) in year n is:<BR>\n" );
document.write( "      * Pn = P0 + r * n <BR>\n" );
document.write( "         * where:<BR>\n" );
document.write( "            * Pn is the amount spent in year n<BR>\n" );
document.write( "            * P0 is the initial amount spent (in 2005) = $38.35<BR>\n" );
document.write( "            * r is the average annual increase = $6.38<BR>\n" );
document.write( "            * n is the number of years after 2005\r<BR>\n" );
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document.write( "   * **Therefore, the explicit formula is:**<BR>\n" );
document.write( "      * Pn = $38.35 + $6.38 * n\r<BR>\n" );
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document.write( "**b) Predict Spending in 2022**\r<BR>\n" );
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document.write( "* Calculate the number of years after 2005:<BR>\n" );
document.write( "   * 2022 - 2005 = 17 years\r<BR>\n" );
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document.write( "* Use the formula to predict spending in 2022:<BR>\n" );
document.write( "   * P17 = $38.35 + $6.38 * 17 <BR>\n" );
document.write( "   * P17 = $38.35 + $108.46<BR>\n" );
document.write( "   * P17 = $146.81\r<BR>\n" );
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document.write( "**The model predicts that $146.81 would be spent on merchandise, apparel, and snacks when watching a Super Bowl game in 2022.**\r<BR>\n" );
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document.write( "**Important Note:** This model assumes a constant linear increase in spending each year. In reality, spending patterns may not follow a perfectly linear trend.<BR>\n" );
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