document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=91829>Question 91829</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Ten years ago your friend invested in a plot of land with the idea of eventually building a summer cottage on it. His plan was to place a \"nest egg\" of $12,000 in a long term Certificate of Deposit which paid 8% interest over a period of 20 years, compounded monthly. At the end of the 20 years, he would use the money to build the cottage. \r<BR>\n" );
document.write( "\n" );
document.write( "The problem was the plot had 8 prairie dogs on it 10 years ago when he acquired the ground.\r<BR>\n" );
document.write( "\n" );
document.write( "This year he made a count of the prairie dogs and found there were 102 on the same plot! A biologist friend assured him that the prairie dogs were growing exponentially according to the law of natural growth, and something needed to be done.<BR>\n" );
document.write( " <BR>\n" );
document.write( "1. Write the formula for natural exponential growth for this particular prairie dog population. <BR>\n" );
document.write( "Hint: Find the \"k\" value for this population, and put it in your formula. <BR>\n" );
document.write( " \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1. Write the formula for natural exponential growth for this particular prairie dog population. <BR>\n" );
document.write( "Hint: Find the \"k\" value for this population, and put it in your formula. <BR>\n" );
document.write( " \r<BR>\n" );
document.write( "\n" );
document.write( "2. Once you have this formula, predict: <BR>\n" );
document.write( "a. approximately how many years from now will the population reach 365 prairie dogs. \r<BR>\n" );
document.write( "\n" );
document.write( "b. approximately how large the population will be 10 years from now. <BR>\n" );
document.write( " <BR>\n" );
document.write( " <BR>\n" );
document.write( " <BR>\n" );
document.write( "3. Write the formula for compound interest and calculate how much money your friend will have on deposit (in the account described above) after 20 years (10 years from now).  <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #66841 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=66841\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> en years ago your friend invested in a plot of land with the idea of eventually building a summer cottage on it. His plan was to place a \"nest egg\" of $12,000 in a long term Certificate of Deposit which paid 8% interest over a period of 20 years, compounded monthly. At the end of the 20 years, he would use the money to build the cottage.<BR>\n" );
document.write( "The problem was the plot had 8 prairie dogs on it 10 years ago when he acquired the ground.<BR>\n" );
document.write( "This year he made a count of the prairie dogs and found there were 102 on the same plot! A biologist friend assured him that the prairie dogs were growing exponentially according to the law of natural growth, and something needed to be done.\r<BR>\n" );
document.write( "\n" );
document.write( "1. Write the formula for natural exponential growth for this particular prairie dog population.<BR>\n" );
document.write( "Hint: Find the \"k\" value for this population, and put it in your formula.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "8*(e^10k) = 102<BR>\n" );
document.write( "e^10k = 102/8<BR>\n" );
document.write( "10k*ln(e) = ln(102/8)<BR>\n" );
document.write( "10k = ln(2.54553); ln of e is 1<BR>\n" );
document.write( "k = 2.54553/10<BR>\n" );
document.write( "k = .255<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The formula A = Ao(e^.255t); Ao=original amt, t=time in years<BR>\n" );
document.write( "2. Once you have this formula, predict:<BR>\n" );
document.write( "a. approximately how many years from now will the population reach 365 prairie dogs.<BR>\n" );
document.write( "102*(e^.255t) = 365<BR>\n" );
document.write( "ln(e^.255t) = ln(365/102)<BR>\n" );
document.write( ".367t*ln(2) = ln(365/102)<BR>\n" );
document.write( ".367t*.693147 = 1.275<BR>\n" );
document.write( ".254385t = 1.275<BR>\n" );
document.write( "t = 5 years<BR>\n" );
document.write( ":<BR>\n" );
document.write( "b. approximately how large the population will be 10 years from now.<BR>\n" );
document.write( "A = 102*(2^.367(10))<BR>\n" );
document.write( "A = 102*(2^3.67); use a good calc here:<BR>\n" );
document.write( "A = 1300 critters 10 yrs from now<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "3. Write the formula for compound interest and calculate how much money your friend will have on deposit (in the account described above) after 20 years (10 years from now).<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Compound Int formula: A = P * <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281+%2B+r%2Fn%29%5Ent ALIGN=MIDDLE  ALT=\"%281+%2B+r%2Fn%29%5Ent\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In 20 yrs:<BR>\n" );
document.write( "A = 12000 * <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281+%2B+.08%2F12%29%5E%2812%2A20%29 ALIGN=MIDDLE  ALT=\"%281+%2B+.08%2F12%29%5E%2812%2A20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "A = 59,121.63<BR>\n" );
document.write( ":<BR>\n" );
document.write( "In 10 yrs:<BR>\n" );
document.write( "A = 12000 * <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281+%2B+.08%2F12%29%5E%2812%2A10%29 ALIGN=MIDDLE  ALT=\"%281+%2B+.08%2F12%29%5E%2812%2A10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "A = 26,635.68<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );