document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=707572>Question 707572</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a tree grows 1.5 meters during the first year of planting.  During each subsequent year, the tree grows 9/10 of the previous year's growth.  When the growth of the tree since planting is 11.35 meters, its age is? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #435763 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39618)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=435763\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A formula has been developed for this.  Terms being like a, ar, ar^2, ar^3,...<BR>\n" );
document.write( "for n terms, the sum of those n terms is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a-ar%5En%29%2F%281-r%29 ALIGN=MIDDLE  ALT=\"%28a-ar%5En%29%2F%281-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "The problem description shows the sum (being 11.35), a=1.5, r=0.9, and the unknown variable is n for the number of years.  You might first want to use the formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5Bn%5D=%28a-ar%5En%29%2F%281-r%29 ALIGN=MIDDLE  ALT=\"S%5Bn%5D=%28a-ar%5En%29%2F%281-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and solve for n.  Once done that, THEN substitute the values.  Working that way, you should get to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5En=%28a-S%281-r%29%29%2Fa ALIGN=MIDDLE  ALT=\"r%5En=%28a-S%281-r%29%29%2Fa\"   DISABLED_style= \"max-width:90%; height:auto;\" >; I am dropping the subscript on S just for convenience.\r<BR>\n" );
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document.write( "Taking logarithms of both sides whatever base you choose,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%2Aln%28r%29=ln%28%28a-S%281-r%29%29%2Fa%29 ALIGN=MIDDLE  ALT=\"n%2Aln%28r%29=ln%28%28a-S%281-r%29%29%2Fa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=ln%28%28a-S%281-r%29%29%2Fa%29%2Fln%28r%29 ALIGN=MIDDLE  ALT=\"n=ln%28%28a-S%281-r%29%29%2Fa%29%2Fln%28r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now just substitute the values.<BR>\n" );
document.write( "log base ten of [(1.5-11.35(1-.9))/1.5]=-0.6138<BR>\n" );
document.write( "log base ten of  0.9=-.045757<BR>\n" );
document.write( "n=13.4 years </SPAN>\n" );
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