document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=301757>Question 301757</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A certain species of bacteria in a laboratory begins with 200 cells and has a half life every 20 minutes. How many cells of the bacteria will be left after 1 hour (60 minutes)? Write an equation to model the problem and then solve your equation for the given value. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #216378 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=216378\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">     A certain species of bacteria in a laboratory begins with 200 cells and has a half life every 20 minutes. How many cells of the bacteria will be left after 1 hour (60 minutes)? Write an equation to model the problem and then solve your equation for the given value.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Use the exponential growth/decay formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28t%29+=+Po%2Ae%5E%28rt%29 ALIGN=MIDDLE  ALT=\"P%28t%29+=+Po%2Ae%5E%28rt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Where<BR>\n" );
document.write( "P(t) is amount after t time<BR>\n" );
document.write( "Po is the initial amount<BR>\n" );
document.write( "r is the rate of growth/decay<BR>\n" );
document.write( "t is time<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Using the first sentence we can determine r:<BR>\n" );
document.write( "(1/2)(200) = 200e^(r*20)<BR>\n" );
document.write( "1/2 = e^(r*20)<BR>\n" );
document.write( "ln(.5) = r*20<BR>\n" );
document.write( "ln(.5)/20 = r<BR>\n" );
document.write( "-.03466 = r<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Our equation then is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28t%29+=+Po%2Ae%5E%28-.03466t%29 ALIGN=MIDDLE  ALT=\"P%28t%29+=+Po%2Ae%5E%28-.03466t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now, we can answer:<BR>\n" );
document.write( "How many cells of the bacteria will be left after 1 hour (60 minutes)? <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28t%29+=+200%2Ae%5E%28-.03466%2A60%29 ALIGN=MIDDLE  ALT=\"P%28t%29+=+200%2Ae%5E%28-.03466%2A60%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P%28t%29+=+25+ ALIGN=MIDDLE  ALT=\"P%28t%29+=+25+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "25 cells left after 60 minutes<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );