document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=183539>Question 183539</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write an exponential function for a graph that includes the given points.<BR>\n" );
document.write( "please help with steps.. please:))\r<BR>\n" );
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document.write( "5.   (0, 0.5), (1, 3)  \r<BR>\n" );
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document.write( "6.   (–1, 5), (0.5, 40) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #137783 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=137783\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll do the first one to get you started\r<BR>\n" );
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document.write( "5)\r<BR>\n" );
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document.write( "Remember, the general equation for any exponential function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=a%2Ab%5Ex ALIGN=MIDDLE  ALT=\"f%28x%29=a%2Ab%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > where \"a\" and \"b\" are constants\r<BR>\n" );
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document.write( "Since we're given the point (0,0.5), this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%280%29=0.5 ALIGN=MIDDLE  ALT=\"f%280%29=0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So this means that\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.5=a%2Ab%5E0 ALIGN=MIDDLE  ALT=\"0.5=a%2Ab%5E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > which simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.5=a%2A1 ALIGN=MIDDLE  ALT=\"0.5=a%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" > or just <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.5=a ALIGN=MIDDLE  ALT=\"0.5=a\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So we now know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=0.5 ALIGN=MIDDLE  ALT=\"a=0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note: I just plugged in the given values into the equation above\r<BR>\n" );
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document.write( "Also, since we have another point (1,3), this tells us that when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%281%29=3 ALIGN=MIDDLE  ALT=\"f%281%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So plug this in to get: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=a%2Ab%5E1 ALIGN=MIDDLE  ALT=\"3=a%2Ab%5E1\"   DISABLED_style= \"max-width:90%; height:auto;\" > which simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=a%2Ab ALIGN=MIDDLE  ALT=\"3=a%2Ab\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=0.5 ALIGN=MIDDLE  ALT=\"a=0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=0.5%2Ab ALIGN=MIDDLE  ALT=\"3=0.5%2Ab\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solve for \"b\" to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=3%2F0.5 ALIGN=MIDDLE  ALT=\"b=3%2F0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=6 ALIGN=MIDDLE  ALT=\"b=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So we now know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=6 ALIGN=MIDDLE  ALT=\"b=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the exponential equation that goes through the points (0, 0.5) and (1, 3) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0.5%2A6%5Ex ALIGN=MIDDLE  ALT=\"y=0.5%2A6%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Note: you can check by plugging in the original \"x\" values to get the f(x) values.\r<BR>\n" );
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document.write( "Here's a visual confirmation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C500%2C-5%2C5%2C-5%2C5%2C%0D%0Agrid%281%29%2C%0D%0Agraph%28500%2C500%2C-5%2C5%2C-5%2C5%2C0.5%2A6%5Ex%29%2C%0D%0Acircle%280%2C0.5%2C0.05%29%2Ccircle%280%2C0.5%2C0.08%29%2C%0D%0Acircle%281%2C3%2C0.05%29%2Ccircle%281%2C3%2C0.08%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Graph of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0.5%2A6%5Ex ALIGN=MIDDLE  ALT=\"y=0.5%2A6%5Ex\"   DISABLED_style= \"max-width:90%; height:auto;\" > through the points (0, 0.5) and (1, 3)\r<BR>\n" );
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