document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=713839>Question 713839</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hoe do I go by obtaining the equation using the format in parentheses?\r<BR>\n" );
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document.write( "A particular species of rare jungle bird is in danger of extinction.  Fifteen years ago, the population was 18,500 and has been decreasing exponentially (A = A0ekt). Today only 5,600 of the reptiles are alive.  \r<BR>\n" );
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document.write( "a. Identify the exponential growth equation that models the population over time.<BR>\n" );
document.write( "b. Using this equation, how many birds would we expect to be alive twenty years from now? <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 #438596 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39621)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=438596\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Using time 0 as 15 years ago, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B0%5D=18500 ALIGN=MIDDLE  ALT=\"A%5B0%5D=18500\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and A=5600.  Use these to find k.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5600=18500%2Ae%5E%28k%2A15%29 ALIGN=MIDDLE  ALT=\"5600=18500%2Ae%5E%28k%2A15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2856%2F185%29=e%5E%28k%2A15%29 ALIGN=MIDDLE  ALT=\"%2856%2F185%29=e%5E%28k%2A15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ln%2856%2F185%29=k%2A15%2A1 ALIGN=MIDDLE  ALT=\"ln%2856%2F185%29=k%2A15%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=%281%2F15%29ln%2856%2F185%29 ALIGN=MIDDLE  ALT=\"k=%281%2F15%29ln%2856%2F185%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28k=-0.0797%29 ALIGN=MIDDLE  ALT=\"highlight%28k=-0.0797%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a.  The decay equation to model the exponential DECAY (not growth) is A=A[0]e^(-0.0797t).  You choice of A[0] depends on when you want to take time point for zero time.  You can choose \"now\" as time=0, and then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B0%5D=5600 ALIGN=MIDDLE  ALT=\"A%5B0%5D=5600\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  For now, current time decay equation, then you can say <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28A=5600%2Ae%5E%28-0.0797t%29%29 ALIGN=MIDDLE  ALT=\"highlight%28A=5600%2Ae%5E%28-0.0797t%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "b.  For twenty years from now, to find how many birds living, (a prediction), use t=20.  Compute A.  Use the equation that was just found. </SPAN>\n" );
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