document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1126129>Question 1126129</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A new model BMW convertible coupe is designed and produced in time to appear in North America in the fall. BMW Corporation has a limited number of new models available. The number of new model BMW convertible coupes purchased in North America is given by N=100,000/1+10e^2t where t is the number of weeks after the BMW is released.\r<BR>\n" );
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document.write( "a. How many new model BMW convertible coupes will have been purchased 3 weeks after the new model becomes available? Round your answer to the nearest integer.\r<BR>\n" );
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document.write( "b. How many after 35 weeks?\r<BR>\n" );
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document.write( "c. What is the maximum number of new model BMW convertible coupes that will be sold in North America? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #742461 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=742461\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula is N = 100,000 / (1 + 10 * e ^ (2 * T).\r<BR>\n" );
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document.write( "T is the number of weeks after the BMW is released.\r<BR>\n" );
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document.write( "there is something wrong with your equation.\r<BR>\n" );
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document.write( "as written, i get the following graph.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/101407.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "when i make 2 * T becomes -2 * T, i get the following graph.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/101408.jpg\" alt=\"$$$\">\r<BR>\n" );
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document.write( "the second graph is what i would expect to see.\r<BR>\n" );
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document.write( "the growth goes up rapidly and then saturates at a maximum level.\r<BR>\n" );
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document.write( "i'd go with y = 100,000 / (1 + 10 * e ^ (-2 * T)).\r<BR>\n" );
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document.write( "using that formula, you get:\r<BR>\n" );
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document.write( "9091 vehicles purchased 3 weeks after launch.\r<BR>\n" );
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document.write( "97,581 vehicles purchased 35 weeks after launch.\r<BR>\n" );
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document.write( "the sale of vehicles saturates at 100,000 vehicles.\r<BR>\n" );
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document.write( "apparently, based on the formula, they expect lots of sales pretty soon after launch but don't expect the total number to get beyond 100,000.\r<BR>\n" );
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document.write( "check your formula.\r<BR>\n" );
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document.write( "i think you'll find that the exponent is negative (e^-2T rather than e^2T).\r<BR>\n" );
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document.write( "note that 1 + 10 * e^-2T is the same as 1 + 10/e^2T.\r<BR>\n" );
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document.write( "as T gets larger, 10 / e^2T becomes smaller until it gets very close to 0, at which time 1 + 10/e^2T becomes very close to 1 and 100,000 / (1 + 10/ e^2T) gets very close to 100,000 / 1 = 100,000.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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