document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=955359>Question 955359</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Table of Data includes:<BR>\n" );
document.write( "Population in the United States as a function of time\r<BR>\n" );
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document.write( "x(years since 1920):{0,10,20,30,40,50,60,70,80,90}<BR>\n" );
document.write( "y(Population in millions): {106,123.2,132.2,151.3,179.3,203.3,226.5,248.7,281.4,308.7}\r<BR>\n" );
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document.write( "Find:\r<BR>\n" );
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document.write( "1). Draw a scatter plot : Done already<BR>\n" );
document.write( "2). Use calculator to find \"the line of best fit\" for this data. Show the equation. <BR>\n" );
document.write( "I found approximately y=2.28x+93.41<BR>\n" );
document.write( "3). What is the slope of the line? I know it is 2.28<BR>\n" );
document.write( "What is the meaning in this application? (Give its units.)<BR>\n" );
document.write( "I believe the meaning is to go up 2.28 and over one. In units I would say roughly twenty but I was hoping for better help in a translation of this answer. I believe I am incorrect.\r<BR>\n" );
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document.write( "4). By hand, develop an exponential model of the form A=Aoe^kt using the data from 1920 and 2000. Round the value of k to 4 decimal places.\r<BR>\n" );
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document.write( "I am unsure on how to do this.\r<BR>\n" );
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document.write( "5). Use your calculator to find \"exponential function of best fit\" for this data. Show the equation.\r<BR>\n" );
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document.write( "y=106.726(1.0124)^x\r<BR>\n" );
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document.write( "6). use function found in 5) to determine the annual percentage rate of growth of the United States\r<BR>\n" );
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document.write( "I assume 1.24% </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #583585 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=583585\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) OK<BR>\n" );
document.write( "2) Yes, correct<BR>\n" );
document.write( "3) Slope in this problem means it the change in population per year so the population was increase at roughly 2.3 million people per year since 1920.<BR>\n" );
document.write( "4) You use two data points to solve for the two unknowns,<BR>\n" );
document.write( "1920  -> 0-106<BR>\n" );
document.write( "2000  -> 80-281.4<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=A%5B0%5De%5E%28kx%29 ALIGN=MIDDLE  ALT=\"A=A%5B0%5De%5E%28kx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=0 ALIGN=MIDDLE  ALT=\"t=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=106 ALIGN=MIDDLE  ALT=\"A=106\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=106=A%5B0%5De%5E%280%29 ALIGN=MIDDLE  ALT=\"106=A%5B0%5De%5E%280%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B0%5D=106 ALIGN=MIDDLE  ALT=\"A%5B0%5D=106\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=80 ALIGN=MIDDLE  ALT=\"x=80\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=281.4 ALIGN=MIDDLE  ALT=\"A=281.4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=281.4=106e%5E%2880x%29 ALIGN=MIDDLE  ALT=\"281.4=106e%5E%2880x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=e%5E%2880t%29=2.654717 ALIGN=MIDDLE  ALT=\"e%5E%2880t%29=2.654717\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80k=ln%282.654717%29 ALIGN=MIDDLE  ALT=\"80k=ln%282.654717%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=ln%282.654717%29%2F80 ALIGN=MIDDLE  ALT=\"k=ln%282.654717%29%2F80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=0.0122 ALIGN=MIDDLE  ALT=\"k=0.0122\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=106e%5E%280.0122x%29 ALIGN=MIDDLE  ALT=\"y=106e%5E%280.0122x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "5) I get a slightly different answer using an online regression calculator <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=107.4367%281.0121%29%5Ex ALIGN=MIDDLE  ALT=\"y=107.4367%281.0121%29%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "6) Yes, that's correct, take your multiplier, subtract 1 and multiply by 100 to get the annual percentage growth rate.\r<BR>\n" );
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