document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1071198>Question 1071198</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The relative growth rate for a certain type of bacteria population is 78% per hour. A small culture has formed and in just 5 hours the count shows to be 34,820 bacteria in the culture. What is the initial number of bacteria in the culture?\r<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 #686167 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=686167\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> discrete compound growth rate formula is:\r<BR>\n" );
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document.write( "f = p * (1+r)^n\r<BR>\n" );
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document.write( "f is the future value.<BR>\n" );
document.write( "p is the present value <BR>\n" );
document.write( "r is the growth rate per time period.<BR>\n" );
document.write( "t is the number of time periods.\r<BR>\n" );
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document.write( "the growth rate is 78% per hour = .78<BR>\n" );
document.write( "the time period is hours.\r<BR>\n" );
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document.write( "in 5 hours, there are 34,820 bacteria in the culture.\r<BR>\n" );
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document.write( "formula becomes\r<BR>\n" );
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document.write( "34820 = p * 1.78^5\r<BR>\n" );
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document.write( "divide both sides of this equation by 1.78^5 and solve for p to get:\r<BR>\n" );
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document.write( "p = 34820 / 1.78^5 = 1948.627177\r<BR>\n" );
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document.write( "in 5 hours, 1948.627177 bacteria will have grown to be equal to 1948.627177 * 1.78^5 = 34820 bacteria.\r<BR>\n" );
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