document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=75640>Question 75640</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0618219560/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\">  When a sky diver jumps from an airplane, her downward velocity, in feet per second, before she opens her parachute is given by v=176(1-0.834) Note there is an exponent of t representing number of seconds that have elapsed since she jumped from the airplane right after 0.834 seconds...I couldn't figure how to type that so...<BR>\n" );
document.write( "  We've found earlier that the terminal velocity for the sky diver is 176 feet per second. How long does it take to reach 90% of terminal velocity? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #54326 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=54326\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=v=176%2A%281-0.834%5Et%29 ALIGN=MIDDLE  ALT=\"v=176%2A%281-0.834%5Et%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "in which v represents velocity in ft/sec of a falling skydiver and t represents the time<BR>\n" );
document.write( "in seconds since the skydiver left the plane.<BR>\n" );
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document.write( "Problem.  How long does it the skydiver to reach 90% (or 0.9) of terminal velocity?<BR>\n" );
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document.write( "So the velocity of the skydiver is to reach 0.9*176 ft/sec. Plug that into the equation<BR>\n" );
document.write( "as the velocity and you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.9%2A176+=+176%2A%281+-+0.834%5Et%29 ALIGN=MIDDLE  ALT=\"0.9%2A176+=+176%2A%281+-+0.834%5Et%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Note that 176 is a factor on both sides of this equation.  Therefore, if you divide both<BR>\n" );
document.write( "sides by 176 you simplify the equation to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.9+=+%281+-+0.834%5Et%29 ALIGN=MIDDLE  ALT=\"0.9+=+%281+-+0.834%5Et%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "and the parentheses can be removed without affecting the equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.9+=+1+-+0.834%5Et ALIGN=MIDDLE  ALT=\"0.9+=+1+-+0.834%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Eliminate the 1 from the right side of this equation by subtracting 1 from both sides to<BR>\n" );
document.write( "get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-0.1+=+-0.834%5Et ALIGN=MIDDLE  ALT=\"+-0.1+=+-0.834%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Finally, multiply both sides by -1 to get rid of the minus signs and then transpose<BR>\n" );
document.write( "(make the left side the right side and the right side the left side).  After you do those two<BR>\n" );
document.write( "steps you are left with:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.834%5Et+=+0.1 ALIGN=MIDDLE  ALT=\"0.834%5Et+=+0.1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Next you take the logarithm of both sides.  (For convenience, use the log to the base 10<BR>\n" );
document.write( "because it's one of the two logarithms on most calculators.) When you do that you get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log%280.834%29%5Et+=+log%280.1%29 ALIGN=MIDDLE  ALT=\"log%280.834%29%5Et+=+log%280.1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Recall from the rules of logarithms that if you take the log of a quantity that has an<BR>\n" );
document.write( "exponent, you can just multiply the exponent times the log of the quantity.  In this case<BR>\n" );
document.write( "the quantity is 0.834 and the exponent is t.  Applying this rule to your equation <BR>\n" );
document.write( "converts it to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2Alog%280.834%29+=+log%280.1%29 ALIGN=MIDDLE  ALT=\"t%2Alog%280.834%29+=+log%280.1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "I guess that now is as good a time as any to grab the calculator and find that log(0.834)<BR>\n" );
document.write( "is equal to -0.078833949 and log(0.1) is equal to -1.  Substitute these two values into<BR>\n" );
document.write( "the equation to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2A%28-0.078833949%29+=+-1 ALIGN=MIDDLE  ALT=\"t%2A%28-0.078833949%29+=+-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now divide both sides of this equation by -0.078833949 and you find the answer to be:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%28-1%29%2F%28-0.078833949%29+=+12.68489031 ALIGN=MIDDLE  ALT=\"t+=+%28-1%29%2F%28-0.078833949%29+=+12.68489031\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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document.write( "So 90% of terminal velocity is reached in about 12.68 seconds ... and that's the answer you<BR>\n" );
document.write( "need.<BR>\n" );
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document.write( "Hope this helps you to understand that logs can be a big help in finding unknown exponents.  <BR>\n" );
document.write( "Whenever you see a variable in an exponent, it may be a clue to thinking about using the<BR>\n" );
document.write( "log function.<BR>\n" );
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document.write( " </SPAN>\n" );
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