document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190384>Question 1190384</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Your company’s new series<BR>\n" );
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document.write( "Avocado Comedy Hour “has been a complete flop, with viewership continuously<BR>\n" );
document.write( "declining at a rate of 30% per month. How long will the average viewer continue to watch<BR>\n" );
document.write( "the show? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849204 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1987)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849204\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The question is asking about how long the *average* viewer will continue to watch the show.  Since viewership is declining at a constant *percentage* rate each month, this is an exponential decay situation.  The average time a viewer continues to watch is related to the reciprocal of the decay rate.\r<BR>\n" );
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document.write( "Here's how to think about it:\r<BR>\n" );
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document.write( "* **Decay Rate:** 30% per month, or 0.30 as a decimal.\r<BR>\n" );
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document.write( "* **Average Viewing Duration:** The average time a viewer continues to watch the show is the inverse of the decay rate.\r<BR>\n" );
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document.write( "Average Viewing Duration = 1 / Decay Rate\r<BR>\n" );
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document.write( "Average Viewing Duration = 1 / 0.30\r<BR>\n" );
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document.write( "Average Viewing Duration = 3.33 months (approximately)\r<BR>\n" );
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document.write( "So, the average viewer will continue to watch the show for approximately 3.33 months.<BR>\n" );
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