document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=173277>Question 173277</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The numbe of people who hear a rumor increases exponentially.  If 20 people start a rumor and if each person who hears the rumor repeats it to two people a day, the number of people N who have heard the rumor after t days is given by the function.<BR>\n" );
document.write( "N(t)=20(3)^t<BR>\n" );
document.write( "a. How many people have heard the rumor after 5 days?<BR>\n" );
document.write( "b. After what amount of time will 1000 people have heard the rumor?<BR>\n" );
document.write( "c. What is the doubling time for the number of people who have heard the rumor?\r<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 #128102 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=128102\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The numbe of people who hear a rumor increases exponentially. If 20 people start a rumor and if each person who hears the rumor repeats it to two people a day, the number of people N who have heard the rumor after t days is given by the function N(t) = 20(3)^t<BR>\n" );
document.write( "a. How many people have heard the rumor after 5 days?<BR>\n" );
document.write( "N(5) = 20*3^5 = 4860<BR>\n" );
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document.write( "b. After what amount of time will 1000 people have heard the rumor?<BR>\n" );
document.write( "1000=20*3^t<BR>\n" );
document.write( "50 = 3^t<BR>\n" );
document.write( "tlog(3) = log50<BR>\n" );
document.write( "t = log(50)/log(30<BR>\n" );
document.write( "t = 3.56 days<BR>\n" );
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document.write( "c. What is the doubling time for the number of people who have heard the rumor?<BR>\n" );
document.write( "N(t) = 20*3^t<BR>\n" );
document.write( "40 = 20*3^t<BR>\n" );
document.write( "2 = 3^t<BR>\n" );
document.write( "tlog(3) = log(2)\r<BR>\n" );
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document.write( "t = log(2)/log(3)<BR>\n" );
document.write( "t = 0.631 days<BR>\n" );
document.write( "====================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " <BR>\n" );
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document.write( "</TD></TR></TABLE>\n" );