document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1081002>Question 1081002</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The monthly income I, in dollars, from a new product is given by <BR>\n" );
document.write( "I(t) = 86000 &#8722; 65000e^&#8722;0.003t<BR>\n" );
document.write( "where t is the time, in months, since the product was first put on the market. (Round your answers to the nearest dollar amount.) <BR>\n" );
document.write( "(a) What was the monthly income after the 50th month and after the 100th month?<BR>\n" );
document.write( "I(50) = $  <BR>\n" );
document.write( "I(100) = $  \r<BR>\n" );
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document.write( "(b) What will the monthly income from the product approach as the time increases without bound?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #695067 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=695067\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula is:\r<BR>\n" );
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document.write( "i(t) = 86000 - 65000 * e^-.003t\r<BR>\n" );
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document.write( "since e^-a = 1/e^a, this formula becomes:\r<BR>\n" );
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document.write( "i(t) = 86000 - 65000 / e^.003t\r<BR>\n" );
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document.write( "you can see that, as t gets extraordinarily large, the value of i(t) gets closer and closer to 86000, because the value of 65000 / e^.003t gets closer and closer to zero.\r<BR>\n" );
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document.write( "to find the income in the 50th and 100th month, just replace t with 50 and 100 respectively to get:\r<BR>\n" );
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document.write( "when t = 50, monthly income = 86000 - 65000 / e^.003*50 = 30053.98153\r<BR>\n" );
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document.write( "when t = 60, monthly income = 86000 - 65000 / e^.003*100 = 37846.81566\r<BR>\n" );
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document.write( "this can be shown graphically below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/051302.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "as t approaches a higher and higher number, the value of y approaches 8600 as shown in the following graph:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/051303.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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