document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=810511>Question 810511</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello! My name is Nevan and I am currently in Alg 2. I have this assignment due in a few days and I got stuck on this problem. I would love a answer and explanation so I know how to do in the future. Much appreciated!  <BR>\n" );
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document.write( "Cockroaches are pretty large bugs that breed very quickly. <BR>\n" );
document.write( "For the purposes of this assignment, we will assume the following:<BR>\n" );
document.write( "Cockroaches breed quickly enough that their population doubles every minute.<BR>\n" );
document.write( "It takes 10 cockroaches to cover one square inch of the ground.<BR>\n" );
document.write( "Assume that you start with a population of 1 cockroach (don't ask how it reproduces). Then the cockroach population is p=2t, where t is measured in minutes.<BR>\n" );
document.write( "Time = t (In Minutes)<BR>\n" );
document.write( "Population of Cockroaches = p<BR>\n" );
document.write( "144 sq. inch in 1 sq. foot<BR>\n" );
document.write( "(I answered 1 and 2 already) <BR>\n" );
document.write( "#1 isn't related to the cockroaches problem. But here it is. \r<BR>\n" );
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document.write( "1)  If the proportionality constant for the birth rate is greater than that for the death rate, are you going to have exponential growth or decay? Explain. \r<BR>\n" );
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document.write( "2) How many Cockroaches cover 1 sq. inch?\r<BR>\n" );
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document.write( "3) How long until there are enough to cover the floor of an 8' by 12' kitchen (make sure to convert from feet to inches)? \r<BR>\n" );
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document.write( "4) How long until they cover the floor of a typical 2000 square foot house? \r<BR>\n" );
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document.write( "5) How long until they cover an area the size of the city of Colorado Springs (about 186 square miles)? \r<BR>\n" );
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document.write( "6) How long until they cover an area the size of Colorado (104, 185 square miles)? \r<BR>\n" );
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document.write( "7) How about an area the size of the United States (3,539,289 square miles including all 50 states plus DC)? \r<BR>\n" );
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document.write( "8) How about covering the world (57,900,000 square miles)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #488211 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=488211\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 3)  8' = 12*8 = 96 inches<BR>\n" );
document.write( "12' = 12*12 = 144 inches<BR>\n" );
document.write( "Area = 96 * 144 = 13824 square inches<BR>\n" );
document.write( "p = 13824 * 10 = 138240 cockroaches<BR>\n" );
document.write( "now we know that the population doubles each minute, we start with 1 cockroach, after 1 minute we have 2, after 2 minutes we have 4, after 3 minutes we have 8<BR>\n" );
document.write( "so we use p = 2^t to give us the population after t minutes<BR>\n" );
document.write( "138240 = 2^t<BR>\n" );
document.write( "we use the definition of logarithm to calculate t<BR>\n" );
document.write( "sooooooo here we go!<BR>\n" );
document.write( "t = log base 2 (138240)<BR>\n" );
document.write( "t = 17.08 minutes<BR>\n" );
document.write( "4) 2000 * 144 = 288000 square inches<BR>\n" );
document.write( "p = 288000 * 10 = 2880000<BR>\n" );
document.write( "t = log base 2 (2880000) = 21.46 minutes<BR>\n" );
document.write( "5) 186 square miles = 27878400 square feet * 186 square miles * 144 square inches = 7.466950656e9 square inches<BR>\n" );
document.write( "p = 7.466950656e9 * 10 = 7.466950656e10<BR>\n" );
document.write( "t = log base 2 (7.466950656e10) = 36.12 minutes<BR>\n" );
document.write( "6) 104185 square miles = 27878400 square feet * 104185 square miles * 144 square inches = 4.18249598976e14 square inches<BR>\n" );
document.write( "p = 4.18249598976e14 * 10 = 4.18249598976e15<BR>\n" );
document.write( "t = log base 2 (4.18249598976e15) =  51.89 minutes<BR>\n" );
document.write( "7) 3539289 square miles = 27878400 square feet * 3539289 square miles * 144 square inches = 1.42084388818944e16 square inches<BR>\n" );
document.write( "p = 1.42084388818944e16 * 10 = 1.42084388818944e17<BR>\n" );
document.write( "t = log base 2 (1.42084388818944e17) = 56.98 minutes<BR>\n" );
document.write( "8) 57900000 square miles = 27878400 square feet *  57900000 square miles * 144 square inches = 2.3243894784e17 square inches<BR>\n" );
document.write( "p = 2.3243894784e17 * 10 = 2.3243894784e18<BR>\n" );
document.write( "t = log base 2 (2.3243894784e18) = 61.01 minutes\r<BR>\n" );
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document.write( " </SPAN>\n" );
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