document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1161510>Question 1161510</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The population of a town is modelled by P(t) = -t^2 + 12t + 4, where P(t) is the number of years since 2000. What is the average rate of change in population on size from 2005 to 2010?\r<BR>\n" );
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document.write( "a) 3000 people/year<BR>\n" );
document.write( "b) 6000 people/year<BR>\n" );
document.write( "c) 10 000 people/year<BR>\n" );
document.write( "d) 15 000 people/year<BR>\n" );
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document.write( "The year 2005 is 5 years after the year 2000<BR>\n" );
document.write( "Plug in t = 5 to find the population in 2005<BR>\n" );
document.write( "P(t) = -t^2 + 12t + 4 <BR>\n" );
document.write( "P(5) = -(5)^2 + 12(5) + 4 <BR>\n" );
document.write( "P(5) = -25 + 60 + 4 <BR>\n" );
document.write( "P(5) = 35 + 4 <BR>\n" );
document.write( "P(5) = 39<BR>\n" );
document.write( "The population in 2005 is 39,000 (assuming P(t) measures the population in thousands of people)\r<BR>\n" );
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document.write( "Repeat for t = 10 to get the population in 2010<BR>\n" );
document.write( "P(t) = -t^2 + 12t + 4 <BR>\n" );
document.write( "P(10) = -10^2 + 12(10) + 4 <BR>\n" );
document.write( "P(10) = -100 + 120 + 4 <BR>\n" );
document.write( "P(10) = 20 + 4 <BR>\n" );
document.write( "P(10) = 24<BR>\n" );
document.write( "The population is now 24,000\r<BR>\n" );
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document.write( "The change in population is 39,000-24,000 = 15,000<BR>\n" );
document.write( "So the population has dropped 15,000 people<BR>\n" );
document.write( "This is over a span of 5 years, so the rate is 15,000/5 = 3,000 people per year.\r<BR>\n" );
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document.write( "In other words, 3000 people are leaving this town each year.\r<BR>\n" );
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document.write( "I would argue it would be better to use a negative number to indicate population decline (and say the rate of change is -3000 people/year); however, your teacher has gone with positive numbers only for the answer choices. Without further context, those answer choices imply population growth.\r<BR>\n" );
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document.write( "Answer: <font color=red size=4>choice A) 3000 people/year</font> are leaving the town.<BR>\n" );
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