document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1144616>Question 1144616</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this problem. \"A researcher is investigating a specimen of bacteria. She finds that the original 1,000 bacteria grew to 2,084,000 in 60 hours. How fast does the bacteria (a) double? (b) quadruple?\". Please kindly explain to me how. Thank you in advance. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #765781 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=765781\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The exponential/decay formula is<BR>\n" );
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document.write( "A = Pe^(rt), A is the ending amount(for example: bacteria, or radioactive element), P is the beginning amount, r is the growth or decay rate, t is time, e is a constant <BR>\n" );
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document.write( "For this problem, the units of t are hours(t = 60), at t = 0, P = 1,000<BR>\n" );
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document.write( "First, we want to find the value for r<BR>\n" );
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document.write( "2084000 = 1000 * e^(r * 60)<BR>\n" );
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document.write( "2084 = e^(r * 60)<BR>\n" );
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document.write( "take natural logarithm of both sides of =<BR>\n" );
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document.write( "60r = ln(2084)<BR>\n" );
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document.write( "r = ln(2084)/60 = 0.1274/hour<BR>\n" );
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document.write( "(a) 2000 = 1000 * e^(0.1274 * t)<BR>\n" );
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document.write( "2 = e^(0.1274t)<BR>\n" );
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document.write( "0.1274t = ln(2)<BR>\n" );
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document.write( "t = ln(2)/0.1274 = 5.44 hours<BR>\n" );
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document.write( "(b) 4000 = 1000 * e^(0.1274 * t)<BR>\n" );
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document.write( "4 = e^(0.1274 * t)<BR>\n" );
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document.write( "t = ln(4)/0.1274 = 10.88 hours<BR>\n" );
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