document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1165703>Question 1165703</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In 2004, there were 3000 iguanas on Galapagos island. Since then, the population of Iguana on the island has increased by 5% each year. In what year will the population first exceed 10,000? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #790178 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=790178\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> in 2004 there are 3000 iguanas.<BR>\n" );
document.write( "the population grows by 5% per year.<BR>\n" );
document.write( "when will the population exceed 10,000?\r<BR>\n" );
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document.write( "formula to use if f = p * (1 + r) ^ n<BR>\n" );
document.write( "f is the future value<BR>\n" );
document.write( "p is the present value<BR>\n" );
document.write( "r is the rate of increase each year.<BR>\n" );
document.write( "n is the number of years.\r<BR>\n" );
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document.write( "formula becomes 10,000 = 3,000 * 1.05 ^ n\r<BR>\n" );
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document.write( "that's because r is equal to 5% per year / 100 = .05 per year.<BR>\n" );
document.write( "1 + r is equal to 1 + .05 = 1.05\r<BR>\n" );
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document.write( "divide both sides of 10,000 = 3,000 * 1.05 ^ n  by 3000 and simplify to get:<BR>\n" );
document.write( "(10/3) = 1.05 ^ n<BR>\n" );
document.write( "take the log of both sides of the equation to get:<BR>\n" );
document.write( "log(10/3) = log(1.05 ^ n)<BR>\n" );
document.write( "by log rules, this becomes:<BR>\n" );
document.write( "log(10/3) = n * log(1.05)<BR>\n" );
document.write( "divide both sides of the equation by log(1.05) to get:<BR>\n" );
document.write( "log(10/3) / log(1.05) = n<BR>\n" );
document.write( "solve for n to get:<BR>\n" );
document.write( "n = log(10/3) / log(1.05) = 24.67654751.<BR>\n" );
document.write( "that's the number of years when the population will be equal to 10,000.<BR>\n" );
document.write( "since:<BR>\n" );
document.write( "x = 0 is the beginning of the first year.<BR>\n" );
document.write( "x = 1 is the end of the first year.<BR>\n" );
document.write( "x = 24 is the end of the twenty-fourth year.<BR>\n" );
document.write( "x = 25 is the end of the twenty-fifth year.<BR>\n" );
document.write( "then:<BR>\n" );
document.write( "the population will exceed 10,000 sometime between the end of the twenty-fourth year and the end of the twenty-fifth year.<BR>\n" );
document.write( "that puts is in the 25th year.\r<BR>\n" );
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document.write( "here's a graph.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2020/092401.jpg\" >\r<BR>\n" );
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document.write( "the points are in (x,y) format.<BR>\n" );
document.write( "x is the end of the year indicated.<BR>\n" );
document.write( "y is the population.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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