document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=296092>Question 296092</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ok, one last one that I need help on.  I get really stuck and frustrated on word problems and this one is overwhelming me.  thxs Lauren\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)?<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 #213421 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=213421\">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. <BR>\n" );
document.write( "(0,2500)<BR>\n" );
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document.write( "The crappie population in 2006 was found to be 4320.<BR>\n" );
document.write( "(3,4320)<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.<BR>\n" );
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document.write( "b) Find the growth function of the form f(t) = yo*b^t that gives the crappie population t years after 2003. The function you have found models <BR>\n" );
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document.write( "2500 = yo<BR>\n" );
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document.write( "4320 = 2500*b^3<BR>\n" );
document.write( "1.729 = b^3<BR>\n" );
document.write( "b = 1.2<BR>\n" );
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document.write( "Model: f(t) = 2500*(1.2)^t<BR>\n" );
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document.write( "c) Predict the crappie population in 2010.<BR>\n" );
document.write( "f(10) = 2500*1.2^10<BR>\n" );
document.write( "f(10) = 15479<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.<BR>\n" );
document.write( "13000 = 2500*1.2^t<BR>\n" );
document.write( "5.2 = 1.2^t<BR>\n" );
document.write( "t*ln(1.2) = ln(5.2)<BR>\n" );
document.write( "t = [ln(5.2)/ln(1.2)]<BR>\n" );
document.write( "t = 17.2995...<BR>\n" );
document.write( "t is appox 17 years<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)?<BR>\n" );
document.write( "Comment: I'll leave that opinion to you.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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