document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=469773>Question 469773</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The \"learning curve\" describes the rate at which a person learns certain tasks. If a person sets a goal of typing N words per minute (wpm), the length of time t (in days) to achieve this goal is given by the following formula. <BR>\n" );
document.write( "t=-62.5ln(1-N/80)\r<BR>\n" );
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document.write( "(a) According to this formula, what is the maximum number of words per minute?\r<BR>\n" );
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document.write( "(b) Solve for N.<BR>\n" );
document.write( "I am trying to remedy this question to no end.Can someone please help me? thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #322270 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=322270\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The answer to (a) hinges on the fact that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+log%28-n%29+ ALIGN=MIDDLE  ALT=\"+log%28-n%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is impossible. There is no exponent with a positive base<BR>\n" );
document.write( "that can give you a negative number.<BR>\n" );
document.write( "Therefore, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1+-+N%2F80+ ALIGN=MIDDLE  ALT=\"+1+-+N%2F80+\"   DISABLED_style= \"max-width:90%; height:auto;\" > cannot be negative.<BR>\n" );
document.write( "This expression becomes negative when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+N+%3E+80+ ALIGN=MIDDLE  ALT=\"+N+%3E+80+\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "so 80 words per minutes is the maximum possible.<BR>\n" );
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document.write( "(b)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+t+=+-62.5%2Aln%281+-+N%2F80%29+ ALIGN=MIDDLE  ALT=\"+t+=+-62.5%2Aln%281+-+N%2F80%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Note here that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ln%28+1+-+N%2F80+%29+ ALIGN=MIDDLE  ALT=\"+ln%28+1+-+N%2F80+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > MUST be negative in<BR>\n" );
document.write( "order that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > come out positive, since (-)x(-) = (+)<BR>\n" );
document.write( "A log can certainly be negative, and it will give you a<BR>\n" );
document.write( "result that is less than 1, but never a negative result<BR>\n" );
document.write( "as I just stated.<BR>\n" );
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document.write( "Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-62.5+ ALIGN=MIDDLE  ALT=\"+-62.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+ln%281+-+N%2F80%29+=+-t%2F62.5+ ALIGN=MIDDLE  ALT=\"+ln%281+-+N%2F80%29+=+-t%2F62.5+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "I can rewrite this as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+e%5E%28-t%2F62.5%29+=+1+-+N%2F80+ ALIGN=MIDDLE  ALT=\"+e%5E%28-t%2F62.5%29+=+1+-+N%2F80+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-N%2F80+=+e%5E%28-t%2F62.5%29+-+1+ ALIGN=MIDDLE  ALT=\"+-N%2F80+=+e%5E%28-t%2F62.5%29+-+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+-80+ ALIGN=MIDDLE  ALT=\"+-80+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+N+=+80%2A%281+-+e%5E%28-t%2F62.5%29%29+ ALIGN=MIDDLE  ALT=\"+N+=+80%2A%281+-+e%5E%28-t%2F62.5%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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