document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=569105>Question 569105</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The earliest mechanical clock appeared around 1350 in europe and would gain or lose and average of 30 minutes per day. After that, accuracy roughly doubled every 30 years. find the predicted accuracy of the clock in the years 1700 and 2000.          </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #367221 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=367221\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The earliest mechanical clock appeared around 1350 in europe and would gain or lose and average of 30 minutes per day. After that, accuracy roughly doubled every 30 years. find the predicted accuracy of the clock in the years 1700 and 2000.<BR>\n" );
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document.write( "\"accuracy...doubled...\" is not a good term.  If the accuracy is 10%, then double that is 20% ??<BR>\n" );
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document.write( "If you mean the error was reduced by a factor of 2:<BR>\n" );
document.write( "1350 - 1700 = 350 yrs<BR>\n" );
document.write( "350/30 =~ 12 periods<BR>\n" );
document.write( "30 mins error * (1/2)^12 = 30/1024 =~ 0.03 min/day = 1.8 seconds/day<BR>\n" );
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document.write( "1350 - 2000 = 650 yrs = 22.7 periods<BR>\n" );
document.write( "30 min*(1/2)^22.7 =~ 4.403E-6 min/day<BR>\n" );
document.write( "=~ 264 microseconds/day<BR>\n" );
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