document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=295222>Question 295222</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I asked a friend of mine who is proficient in math to help me with this well needless to say she has no idea.  Any help would be greatly appreciated.  I know we can only post 4 problems a day the problems I am submitting are homework for college however not graded.  Our homework is optional for us to do, I chose to do it in order to learn so I am able to do the test at the end of the term.  I want to make that clear so the tutors dont think I am looking to have people do my homework for me for a grade.  These problems are not graded.  Thanks for the help \r<BR>\n" );
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document.write( "A new farm pond was stocked with 2500 crappies in 2003.  The crappie population in 2006 was found to be 4320.\r<BR>\n" );
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document.write( "a)	Let t be the number of years after 2003 (in other words t = 0 corresponds to 2003).  Write down the initial crappie population at t = 3.\r<BR>\n" );
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document.write( "b)	Find the growth function of the form f(t) = y0 bt that gives the crappie population t years after 2003.  The function you have found models _________________________.\r<BR>\n" );
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document.write( "c)	Predict the crappie population in 2010.\r<BR>\n" );
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document.write( "d)	In what year will the crappie population reach 13,000?  Give the exact value for t and then use your calculator to approximate t to get the year.\r<BR>\n" );
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document.write( "e)	Are your answers for (c) and (d) consistent with the given population data in your answer to (b)?\r<BR>\n" );
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document.write( "John </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #212802 by </B><A HREF=/tutors/aboutme.mpl?userid=dabanfield><B>dabanfield(803)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=dabanfield><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=212802\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A new farm pond was stocked with 2500 crappies in 2003. The crappie population in 2006 was found to be 4320. <BR>\n" );
document.write( "a) Let t be the number of years after 2003 (in other words t = 0 corresponds to 2003). Write down the initial crappie population at t = 3. <BR>\n" );
document.write( "b) Find the growth function of the form f(t) = y0 bt that gives the crappie population t years after 2003. The function you have found models _________________________. <BR>\n" );
document.write( "c) Predict the crappie population in 2010. <BR>\n" );
document.write( "d) In what year will the crappie population reach 13,000? Give the exact value for t and then use your calculator to approximate t to get the year. <BR>\n" );
document.write( "e) Are your answers for (c) and (d) consistent with the given population data in your answer to (b)? \r<BR>\n" );
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document.write( "ASSUMIMG the population growth is LINEAR the growth function is a line that passes through points (0,2500) and (3,4320). If the growth is exponential the solution is much different.\r<BR>\n" );
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document.write( "The standard form of a line is f(t) = m*t + b where m is the slope and b is the value of f(t) where the line crosses the y axis.\r<BR>\n" );
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document.write( "Since the line passes through (0,2500) and (3,4320) the slope is:\r<BR>\n" );
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document.write( "m = (4320-2500)/(3-0) <BR>\n" );
document.write( "m = 1820/3<BR>\n" );
document.write( "m = 606.66\r<BR>\n" );
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document.write( "So we have y = 606.66*t + b\r<BR>\n" );
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document.write( "When t = 0, y = 2500 so substituting in the equation above we have:\r<BR>\n" );
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document.write( "2500 = 606.66*0 + b<BR>\n" );
document.write( "b = 2500\r<BR>\n" );
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document.write( "The growth function then is y = 606.66*t + 2500\r<BR>\n" );
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document.write( "You can use the equation above to answer c and d:\r<BR>\n" );
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document.write( "c.) for year 2010 t = 7 so:\r<BR>\n" );
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document.write( "y = 606.66*7 + 2500\r<BR>\n" );
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document.write( "d.) 13000 = 606.66*t + 2500<BR>\n" );
document.write( "solve the above for t.<BR>\n" );
document.write( "  </SPAN>\n" );
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