document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1027563>Question 1027563</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose that your foot length L in inches is related to your height h in inches by L = (4/3)sqrt(h). In one (non-leap) year you have a growth spurt in which you grow from 64 inches to 69 inches. Assume that your height changes at a constant rate throughout the year. <BR>\n" );
document.write( "A) Find an expression for dL/dt. <BR>\n" );
document.write( "B) What was the fastest rate of growth that your foot experienced during this time? When did it occur? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #642853 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=642853\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a related rates problem<BR>\n" );
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document.write( "(69 - 64) / 365 = 1/73<BR>\n" );
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document.write( "dh/dt = 1/73 inch/day<BR>\n" );
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document.write( "L = (4/3) * h^(1/2)<BR>\n" );
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document.write( "dL/dt = (2/3) * h^-(1/2) * dh/dt<BR>\n" );
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document.write( "dL/dt = (2/3) * h^-(1/2) * 1/73<BR>\n" );
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document.write( "dL/dt = (2/219) * h^-(1/2)<BR>\n" );
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document.write( "dL/dt decreases from day 1 to day 365<BR>\n" );
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document.write( "here is a graph of dL/dt<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28600%2C+50%2C+1%2C+365%2C+-0.002%2C+0.0012%2C+%282%2F219%29+%2F+%2864+%2B+%28x%2F73%29%29%5E%281%2F2%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "for h = 64 we have dL/dt = 0.001141553 approx 0.00114 inches/day<BR>\n" );
document.write( "for h = 69 we have dL/dt = 0.001099414 approx 0.00109 inches/day<BR>\n" );
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