document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1168672>Question 1168672</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The population of a certain species of birds on an island is limited by the type of habitat required for nesting. The population grows according to the function<BR>\n" );
document.write( "N(t)=28000/5+13.5e^−0.038t, where t is measured in years. Find the initial bird population. What is the maximum population that the environment will support? (i.e. as t→∞ what does N(t) approach?).According to the model, what will the population be in 10 years? Numeric answer only. Make sure to round your answer correctly. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #793245 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=793245\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'm assuming you mean N(t) = 2800/(5+13.5e^−0.038t)<BR>\n" );
document.write( "The initial population is N(0) = 2800/(5+13.5e^0) = 2800/(5+13.5) = 1513.51 -> 1514<BR>\n" );
document.write( "As t→∞, the negative exponential goes to 0. Thus the maximum population is = 28000/5 = 5600<BR>\n" );
document.write( "N(10) = 1967.38 -> 1967 </SPAN>\n" );
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