document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1128142>Question 1128142</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the logistic growth model f(x) = 230/1 + 8e^&#8722;2x^.<BR>\n" );
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document.write( "Find f(0). Round to the nearest tenth. <BR>\n" );
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document.write( "Interpret f(0). \r<BR>\n" );
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document.write( "f(0) represents the rate of growth.\r<BR>\n" );
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document.write( "f(0) represents the half life.    \r<BR>\n" );
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document.write( "f(0) represents the carrying capacity.\r<BR>\n" );
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document.write( "f(0) represents the initial amount.\r<BR>\n" );
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document.write( "f(0) represents the final amount. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #744619 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=744619\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The function as you show it: 230/1 + 8e^&#8722;2x^<br><BR>\n" );
document.write( "You seem to have a misunderstanding of the use of \"^\" to denote exponentiation.  \"3 squared\" is \"3^2\" -- not \"3^2^\"<br><BR>\n" );
document.write( "And in a logistic function, everything after the \"/\" is in the denominator; you need to enclose it in parentheses:  230/(1+8e^(-2x)).<br><BR>\n" );
document.write( "The parentheses around the \"-2x\" exponent are not required; but they help make the expression more clear.<br><BR>\n" );
document.write( "Now to address your questions....<br><BR>\n" );
document.write( "(1) f(0).<br><BR>\n" );
document.write( "When x=0, the exponential in the denominator is 1; the whole denominator is then 1+8 = 9.  So f(0) = 230/9 = 25.6 to the nearest tenth.<br><BR>\n" );
document.write( "(2) As in a huge number of other applications, f(0) means an initial value.<br><BR>\n" );
document.write( "It's not part of your question, but another important number in a logistic function is the carrying capacity, which is the limit of the function value as x gets very large.<br><BR>\n" );
document.write( "As x gets very large, the exponential in the denominator goes to 0, and the whole denominator goes to 1+0=1.  So the carrying capacity is the numerator of the logistic function. </SPAN>\n" );
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