document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=974849>Question 974849</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (Part 1)\r<BR>\n" );
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document.write( "The number of trees in a forest is increasing. Every 16 days the number of trees triples. On June 4,there are 236,196 trees.\r<BR>\n" );
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document.write( "Write an exponential to represent the total number of trees. Let x represent time in 16 day intervals.\r<BR>\n" );
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document.write( "Find the total number of times the tree population has quadrupled when there are 6,377,292 trees.\r<BR>\n" );
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document.write( "How long will it be until there are more than 2 billion trees?<BR>\n" );
document.write( "Determine how long ago the trees appeared if there was initially 4 trees.\r<BR>\n" );
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document.write( "(Part 2)<BR>\n" );
document.write( "Now there is a chemical in the air killing trees, approximately 1/4 of the butterflies are dying each week. Local experts have written the equation representing the number of trees at any time as. 18,921(3/4)^x where x is the number of weeks.\r<BR>\n" );
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document.write( "How many trees will there be after 7 weeks?\r<BR>\n" );
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document.write( "How many weeks will it take for there to be fewer than 100 trees left? Make a table to show how you got your answer.\r<BR>\n" );
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document.write( "My algebra teacher doesn't want to help me and I've been trying to work this problem non stop, please help me, this problem is not very easy (for me). Part 1 and 2 are all related. Thank you in advance :) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #596652 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=596652\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y=ab^x is the basic form.  When x is increased by 16 days, y triples.  6377292/236196  = almost 27.  That is tripling three times<BR>\n" );
document.write( "y=a(1+r)^x<BR>\n" );
document.write( "a=where it starts<BR>\n" );
document.write( "y/a=(1+r)^x<BR>\n" );
document.write( "but y/a=3<BR>\n" );
document.write( "3=(1+r)^x<BR>\n" );
document.write( "Take ln both sides<BR>\n" );
document.write( "ln3= x ln (1+r)<BR>\n" );
document.write( "1.1=16 ln (1+r)<BR>\n" );
document.write( "0.06875=ln (1+r)<BR>\n" );
document.write( "raise both to the e power<BR>\n" );
document.write( "1.0711=1+r<BR>\n" );
document.write( "r=0.0711, the rate of increase.\r<BR>\n" );
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document.write( "236296 (1+0.0711)^x  ;;is the basic equation.<BR>\n" );
document.write( "6377292=236296 (1+0.0711)^x<BR>\n" );
document.write( "Divide to get 26.989=1.0711^x<BR>\n" );
document.write( "ln of both sides  ;; 3.295=x ln 1.0711   ;;; divide by the ln, which is 0.0687<BR>\n" );
document.write( "3.295/0.0687 =x ; x=47.96 days or 48 days.  \r<BR>\n" );
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document.write( "The tree population increases by a factor of 4 in how many days?<BR>\n" );
document.write( "ln4=x (ln(1+.0711);;;  1.386=x *0.0687=20.175 days.<BR>\n" );
document.write( "It has quadrupled twice and a little more.  You can get that de novo by noting it increased by a factor of 27, which is 2 quadruplings but not three.\r<BR>\n" );
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document.write( "2,000,000,000=236296 (1.0711)^x<BR>\n" );
document.write( "divide out  and get  843696=1.0711^x<BR>\n" );
document.write( "take logs both sides  9.0435=x (.0687);  x= 131.63 days.  Note, rounding will make a difference here.\r<BR>\n" );
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document.write( "Does this make sense?  I get a rough count of 8 triplings, which would be 128 days.  Yes, this makes sense.\r<BR>\n" );
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document.write( "4=236296(1+.0711)^x<BR>\n" );
document.write( "0.00001693=1.0711^x<BR>\n" );
document.write( "-10.98= 0.0687 *x<BR>\n" );
document.write( "x=160.<BR>\n" );
document.write( "Therefore, it was 160 days ago.\r<BR>\n" );
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document.write( "That would be 10 triplings.  Or 3^10.  4*(3^10)=236296.\r<BR>\n" );
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document.write( "18921*(0.75)^x;; x=7<BR>\n" );
document.write( "0.75^7= 0.1335<BR>\n" );
document.write( "18921*0.1335=2525.65 or 2526 trees\r<BR>\n" );
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document.write( "You can do this for x^8, x^9, etc.<BR>\n" );
document.write( "or 18921*(0.75)^x=99<BR>\n" );
document.write( "99/18721=0.00523<BR>\n" );
document.write( "ln(0.00523)=x ln (0.75)<BR>\n" );
document.write( "-5.253= x (-0.288)<BR>\n" );
document.write( "x= 18.26 weeks.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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