document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199252>Question 1199252</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At time t = 0 hours, there are 500 bacteria in a favorable growth medium. 5 hours later, there are 2000 bacteria. Assuming exponential growth, what is the growth constant \"k\" for the bacteria?\r<BR>\n" );
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document.write( "A. 0.155<BR>\n" );
document.write( "B. 2.543<BR>\n" );
document.write( "C. 0.135<BR>\n" );
document.write( "D. 0.277<BR>\n" );
document.write( "E. 1.467<BR>\n" );
document.write( "F. 1.866 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833034 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=833034\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> it looks like they used the continuous compounding formula of f = p * e ^ (rt)<BR>\n" );
document.write( "f is the future value = 2000<BR>\n" );
document.write( "p is the present value = 500<BR>\n" );
document.write( "r is the interest rate per hour<BR>\n" );
document.write( "t is the number of hours = 5<BR>\n" );
document.write( "formula becomes:<BR>\n" );
document.write( "formula becomes 2000 = 500 * e ^ (r * 5)<BR>\n" );
document.write( "divide both sides of the equation by 4 to get:<BR>\n" );
document.write( "2000 / 500 =  ^ (r * 5)<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "4 = e ^ (5r)<BR>\n" );
document.write( "take the natural log of both sides of the equation to get:<BR>\n" );
document.write( "ln(4) = ln(e ^ (5r))<BR>\n" );
document.write( "this becomes ln(4) = 5r * ln(e) which becomes ln(e ^ 5r)) = 5r * ln(e)<BR>\n" );
document.write( "this then becomes ln(4) = 5r because ln(e) = 1<BR>\n" );
document.write( "divide both sides of the equation by 5 to get ln(4) / 5 = r<BR>\n" );
document.write( "solve for r to get r = .277 rounded to 3 decimal places.<BR>\n" );
document.write( "looks like selection D is your answer.<BR>\n" );
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