document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=79656>Question 79656</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this problem.I am having a lot of issues with these types of problems.I tried plugging in 200 for P and 3 for t but I still cant get it right.\r<BR>\n" );
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document.write( "The population P of a certain culture is expected to be given by a model P=100e^rt where r is a constant to be determined and t is the number of days since the original population is expected to reach 200 in 3 days.<BR>\n" );
document.write( "a. 0.231<BR>\n" );
document.write( "b. 0.549<BR>\n" );
document.write( "c. 1.098<BR>\n" );
document.write( "d. 1.50 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #57163 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=57163\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The population P of a certain culture is expected to be given by a model P=100e^rt where r is a constant to be determined and t is the number of days since the original population is expected to reach 200 in 3 days.<BR>\n" );
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document.write( "100(e^rt) = P<BR>\n" );
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document.write( "Substitute for t and P<BR>\n" );
document.write( "100(e^(3r)) = 200<BR>\n" );
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document.write( "Divide both sides by 100 and you have:<BR>\n" );
document.write( "e^(3r) = 2<BR>\n" );
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document.write( "Find nat log of both sides:<BR>\n" );
document.write( "ln(e^3r) = ln(2)<BR>\n" );
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document.write( "3r*ln(e) = ln(2); log equiv of exponents<BR>\n" );
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document.write( "3r = .693147; remember ln(e) = 1<BR>\n" );
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document.write( "r = .693147/3<BR>\n" );
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document.write( "r = .231<BR>\n" );
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document.write( "Check solution with a good calc: enter 100(e^(.231*3)) = 199.97 ~ 200 </SPAN>\n" );
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