document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=830622>Question 830622</A>: <I><SPAN STYLE=\"word-break: break-all;\"> After a shipwreck, 120 rats manage to swim from the wreckage to a deserted island.  The rat population on the island grows exponentially, and after 15 months there 280 rats on the island.\r<BR>\n" );
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document.write( "a) Find the function that models the population \"t\" months after the arrival of the rats<BR>\n" );
document.write( "b) What will the population be in 3 years after the shipwreck.<BR>\n" );
document.write( "c) When will the population reach 2000\r<BR>\n" );
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document.write( "Reviewing for a test.  I had trouble with this early, and still struggling with these word problems.  Please help. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #500735 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=500735\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Model generally as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=Ie%5E%28kt%29 ALIGN=MIDDLE  ALT=\"p=Ie%5E%28kt%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, t is in months, I is initial population, k is a constant needing to be found.\r<BR>\n" );
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document.write( "Solve symbolically now, for k.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%28p%29=ln%28I%29%2Bln%28e%5E%28kt%29%29 ALIGN=MIDDLE  ALT=\"ln%28p%29=ln%28I%29%2Bln%28e%5E%28kt%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=ln%28p%29=ln%28I%29%2Bkt%2A1 ALIGN=MIDDLE  ALT=\"ln%28p%29=ln%28I%29%2Bkt%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=kt=ln%28p%29-ln%28I%29 ALIGN=MIDDLE  ALT=\"kt=ln%28p%29-ln%28I%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=kt=ln%28p%2FI%29 ALIGN=MIDDLE  ALT=\"kt=ln%28p%2FI%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28k=%281%2Ft%29ln%28p%2FI%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%28k=%281%2Ft%29ln%28p%2FI%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Compute value of k.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=%281%2F15%29ln%28280%2F120%29 ALIGN=MIDDLE  ALT=\"k=%281%2F15%29ln%28280%2F120%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28k=0.0565%29 ALIGN=MIDDLE  ALT=\"highlight_green%28k=0.0565%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Specific model for this example rat population:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28p=120%2Ae%5E%280.0565%2At%29%29 ALIGN=MIDDLE  ALT=\"highlight%28p=120%2Ae%5E%280.0565%2At%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "REMINDER:  t is in MONTHS </SPAN>\n" );
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