document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=5130>Question 5130</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My question is 2 parts i solved the first part easy but the wecond part is got me stuck\r<BR>\n" );
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document.write( "The growth of a population of bacteria can be bodelled using the function P=2xe^-x where x is measured in hours and p is in millions\r<BR>\n" );
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document.write( "a) find the maximum population and when it occurs - i got 735,758 after 1 hour i think this is right \r<BR>\n" );
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document.write( "b) verify your value by finding the derivative and evaluating the maximum value - im not too sure how to do this and i cant figure out the derivative\r<BR>\n" );
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document.write( "if u could help me that would be sooo good thanks  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #6761 by </B><A HREF=/tutors/aboutme.mpl?userid=khwang><B>khwang(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=khwang><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=6761\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  [quote] P= 2xe^-x where x is measured in hours and p is in millions <BR>\n" );
document.write( "a) find the maximum population and when it occurs - i got 735,758 after 1 hour  [/quote]<BR>\n" );
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document.write( " dP/dx = P' = 2e^-x - 2xe^-x = 2e^-x(1-x) <BR>\n" );
document.write( " Since,e^-x > 0, we have dP/dx = 0 -->x =1.\r<BR>\n" );
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document.write( " Note P\" = -2e^-x(1-x) -2e^-x = 2e^-x(x-3), so P\"(1) < 0.<BR>\n" );
document.write( " By the 2nd derivative test,we see that P has relative max when x = 1.<BR>\n" );
document.write( " And P(1) =0.735759377 *1 million (I really don't care about it)\r<BR>\n" );
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document.write( " Or you use the 1st derivative test by testing P'(1+) < 0 and P'(1-)  > 0.<BR>\n" );
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document.write( " Kenny\r<BR>\n" );
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