document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=675762>Question 675762</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do you solve x-4/x^2+5 for its vertical asymptotes? Also how would you graph y=.25^x and F(x)=3^(3x-2)?Finally how would you Solve this problem. Use the formula P = le kt, that is, assume exponential growth.  A bacterial culture has an initial population of 500.  If its population grows to 6000 in 2 hours, what will it be at the end of 4 hours?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #420047 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=420047\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How do you solve x-4/(x^2+5) for its vertical asymptotes?<BR>\n" );
document.write( "It has no vertical asymptotes because the denominator cannot be zero.<BR>\n" );
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document.write( "Also how would you graph y = 0.25^x and F(x)=3^(3x-2)?<BR>\n" );
document.write( "Plot points to graph each function:<BR>\n" );
document.write( "y = 0.25^x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C0.25%5Ex%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C0.25%5Ex%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "F(x) = 3^(3x-2)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C3%5E%283x-2%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-10%2C10%2C-10%2C10%2C3%5E%283x-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Finally how would you Solve this problem. Use the formula A(t) = Ao*e^(kt), that is, assume exponential growth.<BR>\n" );
document.write( "A bacterial culture has an initial population of 500. If its population grows to 6000 in 2 hours, what will it be at the end of 4 hours?<BR>\n" );
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document.write( "Solve for \"k\":<BR>\n" );
document.write( "6000 = 500*e^(2k)<BR>\n" );
document.write( "e^(2k) = 12<BR>\n" );
document.write( "2k = ln(12)<BR>\n" );
document.write( "k = 1.2425<BR>\n" );
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document.write( "Equation:<BR>\n" );
document.write( "A(t) = 500*e^(1.2425t)<BR>\n" );
document.write( "A(4) = 500*e^(4*1.2425) = 500*144.03 = 72,013 bacteria<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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