document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1087010>Question 1087010</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The number of starbucks stores in the US in 2005 was 8896.  In 2014, there were 11965 Starbucks stores in the US.  Let y be the number of Starbucks stores in the in the year x, where x=0 represents the year 2005.\r<BR>\n" );
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document.write( "a) write a linear equation in slope intercept form that models the growth in number of stores in the US in terns of x.  (hint: the line must pass through the points (0,8896) and (9,,119651)\r<BR>\n" );
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document.write( "b. Use this equation to predict the number of Starbucks stores in the US in the year 2020.<BR>\n" );
document.write( "C. Explain what the slope for this line means int he context of the problem </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #701287 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=701287\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"3\">Part A) \r<BR>\n" );
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document.write( "The two points given are\r<BR>\n" );
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document.write( "A = (x1,y1) = (0,8896)<BR>\n" );
document.write( "B = (x2,y2) = (9,11965)\r<BR>\n" );
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document.write( "m = Slope of line through points A and B\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29 ALIGN=MIDDLE  ALT=\"m+=+%28y%5B2%5D+-+y%5B1%5D%29%2F%28x%5B2%5D+-+x%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%2811965+-+8896%29%2F%289+-+0%29 ALIGN=MIDDLE  ALT=\"m+=+%2811965+-+8896%29%2F%289+-+0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%283069%29%2F%289%29 ALIGN=MIDDLE  ALT=\"m+=+%283069%29%2F%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+341 ALIGN=MIDDLE  ALT=\"m+=+341\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The slope is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+341 ALIGN=MIDDLE  ALT=\"m+=+341\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The y intercept is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+8896 ALIGN=MIDDLE  ALT=\"b+=+8896\"   DISABLED_style= \"max-width:90%; height:auto;\" > as this is the y value when x = 0. See point A.\r<BR>\n" );
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document.write( "So the slope intercept form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+mx%2Bb ALIGN=MIDDLE  ALT=\"y+=+mx%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > turns into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+341x%2B8896 ALIGN=MIDDLE  ALT=\"y+=+341x%2B8896\"   DISABLED_style= \"max-width:90%; height:auto;\" > after performing substitutions or replacements.\r<BR>\n" );
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document.write( "Answer: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+341x%2B8896 ALIGN=MIDDLE  ALT=\"y+=+341x%2B8896\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The graph looks like this\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src=\"https://i.imgur.com/3qvil0E.png\">\r<BR>\n" );
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document.write( "Part B)\r<BR>\n" );
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document.write( "Plug x = 15 into the equation found in part A. Why this x value? Because 15 years have passed since 2005 to get to 2020 (2020-2005 = 15). Keep in mind that x = 0 represents the year 2005\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+341x%2B8896 ALIGN=MIDDLE  ALT=\"y+=+341x%2B8896\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+341%2A15%2B8896 ALIGN=MIDDLE  ALT=\"y+=+341%2A15%2B8896\"   DISABLED_style= \"max-width:90%; height:auto;\" > x has been replaced with 15\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+5115%2B8896 ALIGN=MIDDLE  ALT=\"y+=+5115%2B8896\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+14011 ALIGN=MIDDLE  ALT=\"y+=+14011\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We predict that there will be about 14011 stores in the year 2020 (assuming the growth rate stays the same).\r<BR>\n" );
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document.write( "Answer: 14011\r<BR>\n" );
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document.write( "Part C)\r<BR>\n" );
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document.write( "Slope = rise/run = (change in y)/(change in x)\r<BR>\n" );
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document.write( "The change in y is the change in the number of stores\r<BR>\n" );
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document.write( "The change in x is the change in the year number\r<BR>\n" );
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document.write( "(change in y)/(change in x) = (number of stores)/(number of years) = number of stores per year\r<BR>\n" );
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document.write( "So the slope of 341 means that Starbucks is opening 341 stores per year. In other words, there are 341 new stores opening up every year.\r<BR>\n" );
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document.write( "Obviously this pace can't keep up forever.</font> </SPAN>\n" );
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