document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1096195>Question 1096195</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A population of bacteria has 1175 bacteria in its starting population. The half-life of this particular type of bacteria is 11 days. (This means that every 11 days the population decreases by half.) Write a function B(d) that represents the amount of bacteria B in the population after d days.\r<BR>\n" );
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document.write( "B(d)= <BR>\n" );
document.write( "1175(1/2)<BR>\n" );
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document.write( "In this and every exponential problem, if you want to use decimals use 7 or 8 decimal places. If that doesn't work you will have to use fractions.\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 #710674 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=710674\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula to use with discrete compounding is f = p * (1+r)^n\r<BR>\n" );
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document.write( "when p = 2, the future value will be 1 when the population is halved.\r<BR>\n" );
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document.write( "you get 1 = 2 * (1+r)^n\r<BR>\n" );
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document.write( "r is the rate of growth per time period.<BR>\n" );
document.write( "n is the number of time periods.\r<BR>\n" );
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document.write( "in this problem, our time period is days.\r<BR>\n" );
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document.write( "divide both sides of the equation by 2 to get 1/2 = (1+r)^n\r<BR>\n" );
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document.write( "when n = 11, this formula becomes 1/2 = (1+r)^11\r<BR>\n" );
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document.write( "take the 11th root of both sides of the equation to get (1/2)^(1/11) = 1+r\r<BR>\n" );
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document.write( "subtract 1 from both sides of the equation to get (1/2)^(1/11) - 1 = r\r<BR>\n" );
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document.write( "that's your interest rate per time period.\r<BR>\n" );
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document.write( "(1/2)^(1/11) - 1 is equal to -.0610690893\r<BR>\n" );
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document.write( "that's the growth rate per day.\r<BR>\n" );
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document.write( "test this out with your problem.\r<BR>\n" );
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document.write( "when p = 1175, the formula becomes f = 1175 * (1 - .0610690893) ^ 11.\r<BR>\n" );
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document.write( "this results in f = 587.5\r<BR>\n" );
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document.write( "587.5 * 2 = 1175, therefore 587.5 is exactly 1/2 of 1175.\r<BR>\n" );
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document.write( "if you want to know how much of the bacteria is left after d days, then replace 11 by d in the formula to get:\r<BR>\n" );
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document.write( "f = 1175 * (1 - .0610690893) ^ d\r<BR>\n" );
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document.write( "when d = 11, it's half.\r<BR>\n" );
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document.write( "when d = 22, it's half again.\r<BR>\n" );
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document.write( "when d = 33, it's half again.\r<BR>\n" );
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document.write( "1175 * (1 - .0610690893) ^ 11 = 587.5\r<BR>\n" );
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document.write( "1175 * (1 - .0610690893) ^ 22 = 293.75\r<BR>\n" );
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document.write( "1175 * (1 - .0610690893) ^ 33 = 146.875\r<BR>\n" );
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document.write( "587.5 * 2 = 1175\r<BR>\n" );
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document.write( "293.75 * 2 = 587.5 * 2 = 1175\r<BR>\n" );
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document.write( "146.875 * 2 = 293.75 * 2 = 587.5 * 2 = 1175\r<BR>\n" );
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document.write( "when d = 11, the result is 1/2 of the original.<BR>\n" );
document.write( "when d = 22, the result 1/4 of the original.<BR>\n" );
document.write( "when d = 33, the result is 1/8 of the original.\r<BR>\n" );
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document.write( "the formula you are looking at is:\r<BR>\n" );
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document.write( "f = p * (1 - .0610690893) ^ d\r<BR>\n" );
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