document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1040411>Question 1040411</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help! <BR>\n" );
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document.write( "The fox population in a certain region has a relative growth rate of 7% per year. It is estimated that the population in 2013 was 18,000.\r<BR>\n" );
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document.write( "n(t) = 18,000e^{0.07t}\r<BR>\n" );
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document.write( "After how many years will the fox population reach 22,000? (Round your answer to one decimal place.) \r<BR>\n" );
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document.write( "2. At 8:30 a.m., a coroner was called to the home of a person who had died during the night. In order to estimate the time of death, the coroner took the person's temperature twice. At 9:00 a.m. the temperature was 93.4°F, and at 11:00 a.m. the temperature was 89.2°F. From these two temperatures, the coroner was able to determine that the time elapsed since death and the body temperature were related by the formula\r<BR>\n" );
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document.write( "t=-10ln T-70/98.6-70 \r<BR>\n" );
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document.write( "where t is the time in hours elapsed since the person died and T is the temperature (in degrees Fahrenheit) of the person's body. (This formula is derived from a general cooling principle called Newton's Law of Cooling. It uses the assumptions that the person had a normal body temperature of 98.6°F at death, and that the room temperature was a constant 70°F.) Use the formula to estimate the time of death of the person. (Round your answer to the nearest hour.)\r<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 #655214 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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/cgi-bin/show-face.mpl?user=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=655214\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1. n(t)=18000e^0.07t<BR>\n" );
document.write( "22,000=18000e^0.07t<BR>\n" );
document.write( "divide both sides by 18000<BR>\n" );
document.write( "22/18=e^0.07t=11/9<BR>\n" );
document.write( "Take ln of both sides, because ln reverses e.  ln *e^0.07t=0.07t.  The e disappears<BR>\n" );
document.write( "ln(11/9)=0.07t.  Divide everything by 0.07 and then round at the end.<BR>\n" );
document.write( "t=2.9 years<BR>\n" );
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document.write( "check with 3 years, which should be more:  18000*e^(0.21)=22206<BR>\n" );
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document.write( "2.  t=-10 ln(t-70)/(98.6-70)<BR>\n" );
document.write( "t=-10 ln(93.4-70)/28.6=-10(ln(23.4)/28.6=-10*(-0.200)=2 hours<BR>\n" );
document.write( "t=-10ln(89.2-70)/28.6)=-10ln(19.2/28.6)=3.98 hours.<BR>\n" );
document.write( "Time of death was 7 a.m. This is consistent with the 9 a.m. and 11 a.m. temperatures. </SPAN>\n" );
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