document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204989>Question 1204989</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A population numbers 20,000 organisms initially and grows by 1.1% each year.\r<BR>\n" );
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document.write( "Suppose P represents population, and t the number of years of growth. An exponential model for the population can be written in the form P = a * b^t where a = ? and b = ?. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #841564 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=841564\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> exponential equation is P = a * b ^ t<BR>\n" );
document.write( "a would be equal to 20,000<BR>\n" );
document.write( "b would be equal to 1 + .011 = 1.011<BR>\n" );
document.write( "the equation would become P = 20,000 * 1.011 ^ t.<BR>\n" );
document.write( "the equation can be graphed as shown below.\r<BR>\n" );
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document.write( "in the graph, x takes the place of t.\r<BR>\n" );
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document.write( "at x = 0, the value is 20,000 * 1.011 ^ 0 = 20,000\r<BR>\n" );
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document.write( "at x = 1, the value is 20,000 * 1.011 ^ 1 = 20220\r<BR>\n" );
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document.write( "at x = 10, the value is 20,000 * 1.011 ^ 10 = 22312.157 rounded to 3 decimal places, as in the graph.\r<BR>\n" );
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document.write( "to create b, you take 1.1% and divide it by 100 to get .011.<BR>\n" );
document.write( "that's the decimal equivalent of 1.1%.<BR>\n" );
document.write( "you then add 1 to it to get 1.011.<BR>\n" );
document.write( "that becomes the growth factor.\r<BR>\n" );
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document.write( "20,000 * 1.011 is the same as 20,000 + 20,000 * .011.<BR>\n" );
document.write( "factor out the 20,000 and you get 20,000 * (1 + .011) which becomes 20,000 * 1.011.<BR>\n" );
document.write( "for 1 year out, the value becomes 20,000 * 1.011.<BR>\n" );
document.write( "for 2 years out, the value becomes 20,000 * 1.011 * 1.011 which is equal to 20,000 * 1.011^2<BR>\n" );
document.write( "10 years out is 20,000 * 1.011^10\r<BR>\n" );
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document.write( " </SPAN>\n" );
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