document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=81409>Question 81409</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0534492770/algebrahomeworkh>Precalculus</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> the frog population in a small pond grows exponentially. The current population is 85 frogs, and the relative growth rate is 18% per year. \r<BR>\n" );
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document.write( "a. find function that models the population after t years. <BR>\n" );
document.write( "b. find the projected population after 3 years. <BR>\n" );
document.write( "c. find the number of years required for the frog population to reach 600.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #58311 by </B><A HREF=/tutors/aboutme.mpl?userid=SMM52091><B>SMM52091(3)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=SMM52091><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=58311\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Forumula for this type of problem would be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=P=er%5E%28t%29 ALIGN=MIDDLE  ALT=\"P=er%5E%28t%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where P is the new amount, e is the original, r is the rate, and t is the time. You can create that formula by simply thinking about what the question is asking. If one year goes by, then the new amount of frogs is 18% greater, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=85+%2A+118%25 ALIGN=MIDDLE  ALT=\"85+%2A+118%25\"   DISABLED_style= \"max-width:90%; height:auto;\" > OR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=85+%2A+1.18 ALIGN=MIDDLE  ALT=\"85+%2A+1.18\"   DISABLED_style= \"max-width:90%; height:auto;\" >. If two years go by, then you'd get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=85+%2A+1.18 ALIGN=MIDDLE  ALT=\"85+%2A+1.18\"   DISABLED_style= \"max-width:90%; height:auto;\" > after year one, and then multiply that by 1.18 AGAIN for the second year, so technically <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=85+%2A+1.18+%2A+1.18 ALIGN=MIDDLE  ALT=\"85+%2A+1.18+%2A+1.18\"   DISABLED_style= \"max-width:90%; height:auto;\" > Also known as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+85+%2A+1.18%5E2 ALIGN=MIDDLE  ALT=\"+85+%2A+1.18%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > So....\r<BR>\n" );
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document.write( "a) the formula as a function would be... <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28t%29=er%5Et ALIGN=MIDDLE  ALT=\"f%28t%29=er%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b) plug in to find out the population after 3 years (t)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%283%29+=+%2885%29%281.18%5E3%29 ALIGN=MIDDLE  ALT=\"f%283%29+=+%2885%29%281.18%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%283%29+=+%2885%29%281.643032%29 ALIGN=MIDDLE  ALT=\"f%283%29+=+%2885%29%281.643032%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%283%29+=+139.65772 ALIGN=MIDDLE  ALT=\"f%283%29+=+139.65772\"   DISABLED_style= \"max-width:90%; height:auto;\" > Don't forget to round off, because you can't have .65772 of a frog, thats ridiculous. So 140 frogs after 3 years\r<BR>\n" );
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document.write( "c)plug in to find out the amount of f(t) = 600<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=600+=+%2885%29%281.18%5Et%29 ALIGN=MIDDLE  ALT=\"600+=+%2885%29%281.18%5Et%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.058823529+=+1.18%5Et ALIGN=MIDDLE  ALT=\"7.058823529+=+1.18%5Et\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=log+7.058823529+=+t+log+1.18 ALIGN=MIDDLE  ALT=\"log+7.058823529+=+t+log+1.18\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28log+7.058823529%29%2F%28log+1.18%29+=+t ALIGN=MIDDLE  ALT=\"%28log+7.058823529%29%2F%28log+1.18%29+=+t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11.80729861+=+t ALIGN=MIDDLE  ALT=\"11.80729861+=+t\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "It would take 11.80729861 years to reach 600 frogs. </SPAN>\n" );
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