document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1082986>Question 1082986</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Amy is observing the population of the fish in a pond she built.  She built the pond and populated it with 500 fish.  The population of the fish doubles every year.  Use x to represent the number of years and y to represent the population of the fish.  Which equation represents this situation?  Need help Asap for Highschool!!!\r<BR>\n" );
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document.write( "Y=500(1.02)^x\r<BR>\n" );
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document.write( "Y=502^x\r<BR>\n" );
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document.write( "Y=500(2)^x\r<BR>\n" );
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document.write( "Y=2x<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #696956 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=696956\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the number of fish in the pond starts with 500.\r<BR>\n" );
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document.write( "the population doubles every year.\r<BR>\n" );
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document.write( "this means that, every year, the number of fish in the pond is 2 times the number of fish that were in the pond the previous year.\r<BR>\n" );
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document.write( "so, at the end of the first year, there are 1000 fish in the pond.<BR>\n" );
document.write( "at the end of the second year, there are 2000 fish in the pond.<BR>\n" );
document.write( "at the end of the third year, there are 4000 fish in the pond.<BR>\n" );
document.write( "at the end of the fourth year, there are 8000 fish in the pond.\r<BR>\n" );
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document.write( "1000 is equal to 2 * 500 which is equal to 2^1 * 500<BR>\n" );
document.write( "2000 is equal to 2 * 2 * 500 which is equal to 2^2 * 500<BR>\n" );
document.write( "4000 is equal to 2 * 2 * 2 * 500 which is equal to 2^3 * 500<BR>\n" );
document.write( "8000 is equal to 2 * 2 * 2 * 2 * 500 which is equal to 2^4 * 500<BR>\n" );
document.write( "in year x, therefore, the number of fish in the pond is equal to 2^x * 500.\r<BR>\n" );
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document.write( "that would be equal to selection 3, which is y = 500 * 2^x.\r<BR>\n" );
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document.write( "the general equation is f = p * (1 + r) ^ n\r<BR>\n" );
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document.write( "in your equation:\r<BR>\n" );
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document.write( "p = 500<BR>\n" );
document.write( "r = 1\r<BR>\n" );
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document.write( "why is r = 1?\r<BR>\n" );
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document.write( "the growth rate is 100% each year.<BR>\n" );
document.write( "500 * 2 = 1000 which means the growth is 500 which means the growth rate is equal to 500/500 = 1 * 100 = 100%.<BR>\n" );
document.write( "1000 * 2 = 2000 which means the growth is 1000 which means the growth rate is equal to 1000/1000 = 1 * 100 = 100%\r<BR>\n" );
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document.write( "the formula becomes f = 500 * (1 + 1) ^ n\r<BR>\n" );
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document.write( "simplify and the formula becomes f = 500 * 2 ^ n\r<BR>\n" );
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document.write( "replace f with y and n with x and the formula becomes y = 500 * 2^x\r<BR>\n" );
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document.write( "that's your third selection.\r<BR>\n" );
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