document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=613103>Question 613103</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Bacteria are growing exponentially in an environment of unlimited space and food. The doubling time is 1 hour.\r<BR>\n" );
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document.write( "a) If there are initially x milligrams of bacteria, express the mass of the bacteria as a function of time t. <BR>\n" );
document.write( "f(t)=\r<BR>\n" );
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document.write( "b) Use your answer to (a) to write down an equation whose solution is the time at which there are 3x milligrams of bacteria. Enter your answer in the form, eg . \r<BR>\n" );
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document.write( "c) Solve your equation from (b) <BR>\n" );
document.write( "t =  hours <BR>\n" );
document.write( "d) Your answer to (c) should be between 1 and 2 hours. Check that it is. Do you understand why it has to be ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #385876 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=385876\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Bacteria are growing exponentially in an environment of unlimited space and food. The doubling time is 1 hour. <BR>\n" );
document.write( "a) If there are initially x milligrams of bacteria, express the mass of the bacteria as a function of time t. <BR>\n" );
document.write( "f(t)=x*2^t<BR>\n" );
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document.write( "b) Use your answer to (a) to write down an equation whose solution is the time at which there are 3x milligrams of bacteria. Enter your answer in the form, <BR>\n" );
document.write( "3x = x*2^t<BR>\n" );
document.write( "2^t = 3<BR>\n" );
document.write( "t = ln(3)/ln(2) = 1.585 hrs<BR>\n" );
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document.write( " . <BR>\n" );
document.write( "c) Solve your equation from (b) <BR>\n" );
document.write( "t = 1.585 hours<BR>\n" );
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document.write( "d) Your answer to (c) should be between 1 and 2 hours. Check that it is. Do you understand why it has to be ?<BR>\n" );
document.write( "The quantity is 2x after 1 hr.<BR>\n" );
document.write( "The quantity is 4x after 2 hrs.<BR>\n" );
document.write( "Since the quantity is 3x the time must be between 1 and 2 hours.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "===============<BR>\n" );
document.write( " </SPAN>\n" );
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