document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=107135>Question 107135</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Reaction time problem:  When you are pricked with a pin, there is a short time delay before you say \"ouch!\"  This reaction time varies linearly with the distance between your brain and the place you are pricked.  Dr. Hollers pricks Leslie Morley's finger and toe, and measures reaction times of 15.2 and 22.9 milliseconds, respectively.  (A millisecond is 1/1000 of a second.)  Leslie's finger is 100 cm from the brain, and her toe is 170 cm from the brain.\r<BR>\n" );
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document.write( "a)  Write the particular equation expressing time delay in terms of distance.<BR>\n" );
document.write( "b)  How long would it take Leslie to say \"ouch\" if pricked in the neck, 10 cm from the brain?<BR>\n" );
document.write( "c)  What does the time-intercept equal, and what does it represent in the real world?<BR>\n" );
document.write( "d)  Since the slope is in millisecons per centimeter, its reiprocal is the speed whick nerve impulses travel in centimetes per millisecond.  How fast do the impulses travel in cm/sec?<BR>\n" );
document.write( "e)  Sketch and label the gragh. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #77967 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=77967\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let t=reaction time, x=distance between pin prick and brain, then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T=Ax%2BB ALIGN=MIDDLE  ALT=\"T=Ax%2BB\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "A and B are constants determined by experimentation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T=Ax%2BB ALIGN=MIDDLE  ALT=\"T=Ax%2BB\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15.2=A%28100%29%2BB ALIGN=MIDDLE  ALT=\"15.2=A%28100%29%2BB\"   DISABLED_style= \"max-width:90%; height:auto;\" > Finger data<BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22.9=A%28170%29%2BB ALIGN=MIDDLE  ALT=\"22.9=A%28170%29%2BB\"   DISABLED_style= \"max-width:90%; height:auto;\" > Toe data<BR>\n" );
document.write( "Use equation 2 to solve for B and substitute into 1.<BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22.9=A%28170%29%2BB ALIGN=MIDDLE  ALT=\"22.9=A%28170%29%2BB\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=22.9-A%28170%29 ALIGN=MIDDLE  ALT=\"B=22.9-A%28170%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now substitute,<BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15.2=A%28100%29%2BB ALIGN=MIDDLE  ALT=\"15.2=A%28100%29%2BB\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15.2=A%28100%29%2B%2822.9-A%28170%29%29 ALIGN=MIDDLE  ALT=\"15.2=A%28100%29%2B%2822.9-A%28170%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-7.7=-70A ALIGN=MIDDLE  ALT=\"-7.7=-70A\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=0.11 ALIGN=MIDDLE  ALT=\"A=0.11\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now that you know A, find B. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=22.9-A%28170%29 ALIGN=MIDDLE  ALT=\"B=22.9-A%28170%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=22.9-%280.11%29%28170%29 ALIGN=MIDDLE  ALT=\"B=22.9-%280.11%29%28170%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B=4.2 ALIGN=MIDDLE  ALT=\"B=4.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Therefore your equation is<BR>\n" );
document.write( "a.)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T=0.11x%2B4.2 ALIGN=MIDDLE  ALT=\"T=0.11x%2B4.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where x is measured in cm, and T is measured in milliseconds. <BR>\n" );
document.write( "b.) When x=10 cm, then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T=0.11x%2B4.2 ALIGN=MIDDLE  ALT=\"T=0.11x%2B4.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T=0.11%2810%29%2B4.2 ALIGN=MIDDLE  ALT=\"T=0.11%2810%29%2B4.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=T=5.3 ALIGN=MIDDLE  ALT=\"T=5.3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "T=5.3 milliseconds<BR>\n" );
document.write( "c.)The time equation is broken up into two sections:length dependent part <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.11x ALIGN=MIDDLE  ALT=\"0.11x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the length independent part <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.2 ALIGN=MIDDLE  ALT=\"4.2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The length dependent part is the time it takes the signal to travel from the injury to the brain. The length independent part is the time required for the brain to recognize there is an injury and to send a signal to your speech center and then make the sound, \"Ouch\".<BR>\n" );
document.write( "d.) Slope = 0.11 ms/cm, velocity,v, is 1/Slope.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=1cm%2F0.11ms ALIGN=MIDDLE  ALT=\"v=1cm%2F0.11ms\"   DISABLED_style= \"max-width:90%; height:auto;\" >x<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000m%2Fs ALIGN=MIDDLE  ALT=\"1000m%2Fs\"   DISABLED_style= \"max-width:90%; height:auto;\" >= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9090 ALIGN=MIDDLE  ALT=\"9090\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm/sec<BR>\n" );
document.write( "e.)\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+300%2C+300%2C+-10%2C+190%2C+-10%2C+30%2Cgrid%28+10%29%2Cgreen%28line%28+0%2C4.2%2C+200%2C+26.2%29%29%2Ccircle%28100%2C15.2%2C3%29%2Ccircle%28170%2C22.9%2C3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );