document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=92213>Question 92213</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A.)  Linear Growth A town has a fixed increase in population growth number of population increase each year. population 1897. Find the growth rates for the following\r<BR>\n" );
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document.write( "I don't get this at all?\r<BR>\n" );
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document.write( "Year (t)	Population (P)<BR>\n" );
document.write( "t = 0           Po = 1897<BR>\n" );
document.write( "(2010)	\r<BR>\n" );
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document.write( "t = 1<BR>\n" );
document.write( "(2011)	<BR>\n" );
document.write( "t = 2<BR>\n" );
document.write( "(2012)	<BR>\n" );
document.write( "t = 3<BR>\n" );
document.write( "(2013)	<BR>\n" );
document.write( "t = 6<BR>\n" );
document.write( "(2016)	\r<BR>\n" );
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document.write( "B.)   Find a linear equation in the form P = mt + b (y = mx + b), which gives the population, P, t years from 2010. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #67063 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=67063\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If I understand your wording correctly, you are told that the initial population of the <BR>\n" );
document.write( "town in 2010 is 1897. Each year that passes the town  adds another 1897 persons.<BR>\n" );
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document.write( "So the population is projected to be:<BR>\n" );
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document.write( "In 2010 ... t=0 ... Population = 1897 <=== this is Po<BR>\n" );
document.write( "In 2011 ... t=1 ... Population = 3794<BR>\n" );
document.write( "In 2012 ... t=2 ... Population = 5691<BR>\n" );
document.write( "In 2013 ... t=3 ... Population = 7588<BR>\n" );
document.write( "In 2014 ... t=4 ... Population = 9485<BR>\n" );
document.write( "In 2015 ... t=5 ... Population = 11382<BR>\n" );
document.write( "In 2016 ... t=6 ... Population = 13279<BR>\n" );
document.write( "and so on ...<BR>\n" );
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document.write( "The rate of change is 1897 per year. This will be the slope of the graph because each year<BR>\n" );
document.write( "that passes results in an increase of 1897 in the population.<BR>\n" );
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document.write( "Using the equation form P=mt+b, we can replace m with 1897 to get:<BR>\n" );
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document.write( "P = 1897*t + b<BR>\n" );
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document.write( "in which t is the year of interest minus 2010.<BR>\n" );
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document.write( "Suppose our year of interest is 2010. Then t = 2010 - 2010 = 0<BR>\n" );
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document.write( "We know that in 2010 the population P is 1897. So we can substitute 1897 for P and 1897<BR>\n" );
document.write( "for m to make the equation become:<BR>\n" );
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document.write( "1897 = 1897*0 + b<BR>\n" );
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document.write( "Do the multiplication on the right side to get:<BR>\n" );
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document.write( "1897 = 0 + b<BR>\n" );
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document.write( "This tells us that b is 1897. Substitute this value for b in the equation, and it becomes:<BR>\n" );
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document.write( "P = 1897t + 1897<BR>\n" );
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document.write( "Let's check this out. Suppose the year we are interested in finding the population<BR>\n" );
document.write( "is 2015 ... 5 years after 2010 so that t = 5. Substitute t = 5 and the equation becomes:<BR>\n" );
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document.write( "P = 1897*5 + 1897 = 9485 + 1897 = 11382<BR>\n" );
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document.write( "That is exactly as our table above said it would be.<BR>\n" );
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document.write( "So all you have to do is pick a year for wish you want to find the population. Subtract<BR>\n" );
document.write( "2010 from that year. Use the result of that subtraction as the value of t in the equation:<BR>\n" );
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document.write( "P = 1897*t + 1897<BR>\n" );
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document.write( "For example. Suppose the year you are interested in finding the population for is 2030.<BR>\n" );
document.write( "Subtract 2010 from 2030 and get 20 for the value of t. Substituting 20 for t results in<BR>\n" );
document.write( "the equation becoming:<BR>\n" );
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document.write( "P = 1897*20 + 1897<BR>\n" );
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document.write( "The multiplication on the right side makes the equation become:<BR>\n" );
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document.write( "P = 37940 + 1897 = 39837<BR>\n" );
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document.write( "In 2030 the population will be 39,837.<BR>\n" );
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document.write( "Hope this helps you to understand the problem a little better. </SPAN>\n" );
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