document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1111815>Question 1111815</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the population of a Fantasy Island is growing at 2% per year and if its population in the year 2006 was 2,200,000. <BR>\n" );
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document.write( "a. Determine an exponential equation representing its population as a function of time. <BR>\n" );
document.write( "b. Determine its population in 2020.<BR>\n" );
document.write( "c. Determine what was its population in 2004.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #726838 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=726838\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The exponential growth or decay formula is<BR>\n" );
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document.write( "a) y(t) = a * e^(kt), y(t) is value at time t, a is the beginning value, k is the rate of growth(k>0) or decay(k<0), t is time, e is euler's number approximately 2.71828<BR>\n" );
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document.write( "b) t = 2020 - 2006 = 14 <BR>\n" );
document.write( "population(t=14) = 2200000 * (2.71828)^(0.02 * 14) = 2910885.587 = 2,910,886<BR>\n" );
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document.write( "c) t = 2006 - 2004 = 2<BR>\n" );
document.write( "population(t=2) = 2200000 * (2.71828)^(-0.02 * 2) = 2113736.76 = 2,113,737<BR>\n" );
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