document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1026385>Question 1026385</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This exercise uses the population growth model. \r<BR>\n" );
document.write( "\n" );
document.write( "A culture starts with 8700 bacteria. After 1 hour the count is 10,000.<BR>\n" );
document.write( "(a) Find a function that models the number of bacteria n(t) after t hours. (Round your r value to three decimal places.) <BR>\n" );
document.write( "n(t) =  <BR>\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "(b) Find the number of bacteria after 2 hours. (Round your answer to the nearest hundred.) <BR>\n" );
document.write( "_____bacteria \r<BR>\n" );
document.write( "\n" );
document.write( "(c) After how many hours will the number of bacteria double? (Round your answer to one decimal place.) <BR>\n" );
document.write( "_____hr </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #641630 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39620)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=641630\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> p for population<BR>\n" );
document.write( "x for time in hours<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=8700%2Ae%5E%28kx%29 ALIGN=MIDDLE  ALT=\"p=8700%2Ae%5E%28kx%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Solve the model for k.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28p%29=ln%288700%29%2Bkx%2Aln%28e%29 ALIGN=MIDDLE  ALT=\"ln%28p%29=ln%288700%29%2Bkx%2Aln%28e%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=kx%2A1=ln%28p%29-ln%288700%29 ALIGN=MIDDLE  ALT=\"kx%2A1=ln%28p%29-ln%288700%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=%281%2Fx%29%28ln%28p%29-ln%288700%29%29 ALIGN=MIDDLE  ALT=\"k=%281%2Fx%29%28ln%28p%29-ln%288700%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Substitute the point  (1,10000).<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=%281%2F1%29%28ln%2810000%29-ln%288700%29%29 ALIGN=MIDDLE  ALT=\"k=%281%2F1%29%28ln%2810000%29-ln%288700%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=ln%2810000%29-ln%288700%29 ALIGN=MIDDLE  ALT=\"k=ln%2810000%29-ln%288700%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=0.13926 ALIGN=MIDDLE  ALT=\"k=0.13926\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----which you might want only to three significant figures, or maybe just two.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "If you want p after 2 hours, you could simply use   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10000%2810000%2F8700%29 ALIGN=MIDDLE  ALT=\"10000%2810000%2F8700%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and it SHOULD be the same as  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8700%2Ae%5E%280.139%2A2%29 ALIGN=MIDDLE  ALT=\"8700%2Ae%5E%280.139%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >;  just try it /them and see.  The model more specifically is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28p=8700%2Ae%5E%280.139%2Ax%29%29 ALIGN=MIDDLE  ALT=\"highlight%28p=8700%2Ae%5E%280.139%2Ax%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Find x for how long to double.<BR>\n" );
document.write( "Take logs of both sides and solve for x.<BR>\n" );
document.write( "More simply,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2=1%2Ae%5E%280.13926%2Ax%29 ALIGN=MIDDLE  ALT=\"2=1%2Ae%5E%280.13926%2Ax%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---------start from this form. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );