document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=485419>Question 485419</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have 3 questions that needs to be answered using a graph, but I am unable to copy and paste alone with the questions. I will explain the graph. Here are the instructions and questions:\r<BR>\n" );
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document.write( "The following graph shows data regarding the population of Rochester, New York. Original projections predicted the same population in half the number of years.\r<BR>\n" );
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document.write( " Answer the following questions. Please show all of your work. \r<BR>\n" );
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document.write( "At what rate was the population changing? <BR>\n" );
document.write( "At what rate did the projections predict the population would change? <BR>\n" );
document.write( "What was the predicted population in 2003?\r<BR>\n" );
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document.write( "the graph shows the population started at 350,000; declined to 300,000 in 2 years. Then decline again to 250,000 in 4 years. \r<BR>\n" );
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document.write( "Thank you for your help.<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 #332055 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=332055\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i'll work in thousands.<BR>\n" );
document.write( "you start at 350 thousand in year 0, drop to 300 thousand in year 2 and drop to 250 thousand in year 4.<BR>\n" );
document.write( "you are dropping 50 thousand every 2 years or 25000 a year.<BR>\n" );
document.write( "your equation is y = -25x + 350<BR>\n" );
document.write( "your graph looks like this.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-1%2C5%2C-50%2C450%2C-25x%2B350%2C350%2C300%2C250%29%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-1%2C5%2C-50%2C450%2C-25x%2B350%2C350%2C300%2C250%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "the horizontal lines are at y = 350, 300, and 250 thousand.<BR>\n" );
document.write( "when x = 0, y = 350 thousand<BR>\n" );
document.write( "when x = 2, y = 300 thousand<BR>\n" );
document.write( "when x = 4, y = 250 thousand<BR>\n" );
document.write( "the problem statement says:<BR>\n" );
document.write( "original projections predicated the same population in half the number of years.<BR>\n" );
document.write( "this means that Rochester was projected to have 300 thousand in 1 year and 250 thousand in 2 years.<BR>\n" );
document.write( "that would be a drop in population of 50 thousand per year.<BR>\n" );
document.write( "the equation for that would be y = -50x + 350<BR>\n" );
document.write( "add that equation to the graph and it looks like what you see below.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-1%2C5%2C-50%2C450%2C-25x%2B350%2C-50x%2B350%2C350%2C300%2C250%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-1%2C5%2C-50%2C450%2C-25x%2B350%2C-50x%2B350%2C350%2C300%2C250%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "you can see that the first equation crosses the 300 thousand line in 2 years and the 250 thousand line in 4 years, while the second equation crosses the 300 thousand line in 1 year and the 250 thousand line in 2 years.<BR>\n" );
document.write( "answers to your questions are below:<BR>\n" );
document.write( "At what rate was the population changing?<BR>\n" );
document.write( "it changed at the rate of minus 25 thousand per year.<BR>\n" );
document.write( "At what rate did the projections predict the population would change?<BR>\n" );
document.write( "the projections predicted the population would change at the rate of minus 50 thousand per year.<BR>\n" );
document.write( "What was the predicted population in 2003? <BR>\n" );
document.write( "it depends on when you started.  <BR>\n" );
document.write( "the predicted population decreased by 50 thousand per year.<BR>\n" );
document.write( "it started at 350 thousand.<BR>\n" );
document.write( "if the start year is 2000, then 2003 is 3 years from that and the predicted population would be 350 thousand minus 3*50 thousand = 350 thousand minus 150 thousand = 200 thousand.<BR>\n" );
document.write( "find the start year and subtract it from 2003.  multiply 50 thousand by the number of years and subtract it from 350 thousand.\r<BR>\n" );
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