document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=6725>Question 6725</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Dear Sir/Madam, <BR>\n" );
document.write( "I am confronted with the following problem: <BR>\n" );
document.write( "\"Find an exponential function of the form f(x) = a * e^(b/x) + c that has y-intercept (0,5), a horizontal asymptote y = 3, and whose graph passes through the point (4,10).\"\r<BR>\n" );
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document.write( "I don't know how to use the fact that the function has a horizontal asymptote at y = 3 in order to solve this question. I know that the horizontal asymptote means that the function will never be equal to 3, but other than that, I don't know how to use it. Can you help me?<BR>\n" );
document.write( "Thanks in advance.<BR>\n" );
document.write( "Regards,<BR>\n" );
document.write( "-Mike </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #3715 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=3715\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  Find an exponential function of the form f(x) = a * e^(b/x) + c that has y-intercept (0,5), a horizontal asymptote y = 3, and whose graph passes through the point (4,10).\" <BR>\n" );
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document.write( " \"a horizontal asymptote y = 3\" means \" when x-->+/- oo, y-->3\"<BR>\n" );
document.write( " (you are right my can never be 3.]\r<BR>\n" );
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document.write( " In this exponential case, if b> 0 and lim f(x) exists as x-->+oo,<BR>\n" );
document.write( " then lim f(x)--> a*0 + c= c, so y=c=3.<BR>\n" );
document.write( " When b > 0, lim f(x) --> c=3 as x-->-oo.<BR>\n" );
document.write( " We claim, c = 3.\r<BR>\n" );
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document.write( " Now, f(0) = a*1 + 3 = 5, so a = 2.<BR>\n" );
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document.write( " Next, use f(4) = 2e^(b/4) + 3 = 10, or e^(b/4) = 7/2.<BR>\n" );
document.write( " So  b = 4ln(7/2) [stop here, don't make ugly decimals or approx.]<BR>\n" );
document.write( " Answer f(x) = 2 e^(4/x * ln(7/2)) +3.\r<BR>\n" );
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document.write( " [Note ; e^(4/xln(7/2)) = (7/2)^(4/x)]\r<BR>\n" );
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document.write( " Kenny\r<BR>\n" );
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document.write( " PS: It is important for me that you posted these two questions in<BR>\n" );
document.write( " wrong category. Never happen again!<BR>\n" );
document.write( "  </SPAN>\n" );
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