document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203682>Question 1203682</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The hourly wage of some Toyota assembly line workers increased annually by the same percentage if their wage went from 7.10 to 20.08 in 12 years what is the doubling time </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839440 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=839440\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Refer to the steps tutor @Edwin has provided to determine that r = 0.09 = 9% approximately. \r<BR>\n" );
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document.write( "Another approach would be to find the positive root of the function <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=7.10%281%2Bx%29%5E%2812%29-20.08 ALIGN=MIDDLE  ALT=\"f%28x%29=7.10%281%2Bx%29%5E%2812%29-20.08\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use a graphing tool like a TI83/TI84, Desmos, or GeoGebra. <BR>\n" );
document.write( "The root finding feature quickly locates the positive x intercept to be roughly x = 0.09\r<BR>\n" );
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document.write( "Then we can use the <a  rel=nofollow HREF=\"https://en.wikipedia.org/wiki/Rule_of_72\">rule of 72</a> shortcut.<BR>\n" );
document.write( "We divide 72 over the r value, in which we have removed the percent sign. Do not use the decimal form.\r<BR>\n" );
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document.write( "doubling time = 72/(r value without percent sign) <BR>\n" );
document.write( "doubling time = 72/9 <BR>\n" );
document.write( "doubling time = 8 years\r<BR>\n" );
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document.write( "This shortcut gives us an approximation rather than the exact answer. <BR>\n" );
document.write( "But sometimes all that's needed is a good enough approximation.\r<BR>\n" );
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document.write( "A more accurate doubling time formula is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28ln%282%29%29%2F%28ln%281%2Br%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28ln%282%29%29%2F%28ln%281%2Br%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where the 2 in ln(2) refers to doubling. <BR>\n" );
document.write( "Replace 2 with 3 if you want to know how long it takes for your money to triple for instance.\r<BR>\n" );
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document.write( "If r = 0.09, then we'll get the following doubling time<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28ln%282%29%29%2F%28ln%281%2Br%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28ln%282%29%29%2F%28ln%281%2Br%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28ln%282%29%29%2F%28ln%281%2B0.09%29%29 ALIGN=MIDDLE  ALT=\"t+=+%28ln%282%29%29%2F%28ln%281%2B0.09%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+8.0432 ALIGN=MIDDLE  ALT=\"t+=+8.0432\"   DISABLED_style= \"max-width:90%; height:auto;\" > approximately, which is fairly close to t = 8 we got earlier.<BR>\n" );
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