document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1085341>Question 1085341</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Cate purchases $1600 worth of stock and her broker estimates it will increase in value by 4.2% each year. after about how many years will the value of Cate's  stock be about $2000?<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 #699451 by </B><A HREF=/tutors/aboutme.mpl?userid=addingup><B>addingup(3677)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=addingup><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=addingup><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=699451\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1600(1+0.042)^t = 2000<BR>\n" );
document.write( "(1+0.042)^t = 2000/1600 = 5/4<BR>\n" );
document.write( "log((1.042)^t) = log(5/4)<BR>\n" );
document.write( "the log of a number raised to a power is equal to the power times the log of the number:<BR>\n" );
document.write( "t*log(1.042) = log(5/4<BR>\n" );
document.write( "t = log(5/4)/log(1.042)<BR>\n" );
document.write( "change of base: log(a)/log(b) = log_b(a)<BR>\n" );
document.write( "t = log_1.042(5/4) = 5.42 years<BR>\n" );
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document.write( "check:<BR>\n" );
document.write( "1600(1+0.042)^5.42 = 2000 correct\r<BR>\n" );
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