document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=811763>Question 811763</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can I please get help to answer the following question with full working.\r<BR>\n" );
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document.write( "The sales of a new electronic gadget are growing exponentially such that a<BR>\n" );
document.write( "total of 10000 gadgets were sold in 2000 and 82700 gadgets were sold in<BR>\n" );
document.write( "2002. If this trend continues, in what year will sales of the gadget reach or<BR>\n" );
document.write( "exceed 500 000? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #488881 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=488881\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Take year 2000 to be time of 0, for convenience.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=10000e%5E%28kt%29 ALIGN=MIDDLE  ALT=\"y=10000e%5E%28kt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  for t as time in years since 2000, y is the sales count of items sold at time t, and k is a constant.\r<BR>\n" );
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document.write( "Solve symbolically for k.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28y%29=ln%2810000%29%2Bkt%2Aln%28e%29 ALIGN=MIDDLE  ALT=\"ln%28y%29=ln%2810000%29%2Bkt%2Aln%28e%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28y%29-ln%2810000%29=kt ALIGN=MIDDLE  ALT=\"ln%28y%29-ln%2810000%29=kt\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=%28ln%28y%29-ln%2810000%29%29%2Ft ALIGN=MIDDLE  ALT=\"k=%28ln%28y%29-ln%2810000%29%29%2Ft\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Use the point for year 2002, for t=2, to get a value for k.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=%28ln%2882700%29-ln%2810000%29%29%2F2 ALIGN=MIDDLE  ALT=\"k=%28ln%2882700%29-ln%2810000%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=2.1126%2F2 ALIGN=MIDDLE  ALT=\"k=2.1126%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28k=1.056%29 ALIGN=MIDDLE  ALT=\"highlight%28k=1.056%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The model equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=10000e%5E%281.056%2At%29%29 ALIGN=MIDDLE  ALT=\"highlight%28y=10000e%5E%281.056%2At%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----\r<BR>\n" );
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document.write( "Your question to answer is, find t for y=500000.<BR>\n" );
document.write( "Looking back at solving for k, the step was found,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28y%29-ln%2810000%29=kt ALIGN=MIDDLE  ALT=\"ln%28y%29-ln%2810000%29=kt\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "from which we can easily step to <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%28ln%28y%29-ln%2810000%29%29%2Fk ALIGN=MIDDLE  ALT=\"t=%28ln%28y%29-ln%2810000%29%29%2Fk\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and then substituting for y, and k,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%28ln%28500000%29-ln%2810000%29%29%2F1.056 ALIGN=MIDDLE  ALT=\"t=%28ln%28500000%29-ln%2810000%29%29%2F1.056\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28t=3.704%29 ALIGN=MIDDLE  ALT=\"highlight%28t=3.704%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > years since 2000, or some late in the year 2003, or very early in year 2004.\r<BR>\n" );
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document.write( "Think about that time value.  2000+3.7=2003.7, which could potentially be early in year 2004. </SPAN>\n" );
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