document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1080293>Question 1080293</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A GROUP OF SCIENTISTS STUDDIED THE EFFECT OF a chemical on various strands of bacteria. strain a started with 6000 cells and decreased at a constant rate of 2000 cells per hour after the chemical was applied. strain b started with 2000 cells and decreased at a constant rate of 100 cells per hour after the chemical was applied. when will the strains have the same number of cells explain.<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 #694497 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=694497\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the general formula is:\r<BR>\n" );
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document.write( "f = p + r * x\r<BR>\n" );
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document.write( "f is the future value<BR>\n" );
document.write( "p is the present value<BR>\n" );
document.write( "r is the rate of change in the number of cells per hour.<BR>\n" );
document.write( "x is the number of hours.\r<BR>\n" );
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document.write( "the first strain starts with 6000 cells and decreases at the rate of 2000 cells per hour.\r<BR>\n" );
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document.write( "the formula would be f = 6000 - 2000 * x\r<BR>\n" );
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document.write( "f is the future value<BR>\n" );
document.write( "6000 is the present value<BR>\n" );
document.write( "-2000 is the rate of change per hour.<BR>\n" );
document.write( "x is then number of hours.\r<BR>\n" );
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document.write( "note that 6000 + (-2000 * x) is the sme as 6000 - 2000 * x\r<BR>\n" );
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document.write( "the second strain starts with 2000 cells and decreases at the rate of 100 cells per hour.\r<BR>\n" );
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document.write( "the formula would be f = 2000 - 100 * x\r<BR>\n" );
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document.write( "f is the future value<BR>\n" );
document.write( "2000 is the present value<BR>\n" );
document.write( "-100 is the rate of change per hour.<BR>\n" );
document.write( "x is the number of hours.\r<BR>\n" );
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document.write( "note that 2000 + (-100 * x) is the same as 2000 = 100 * x\r<BR>\n" );
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document.write( "they will have the same number of cells when the future value of the first formula is equal to the future value of the second formula.\r<BR>\n" );
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document.write( "that happens when 6000 - 2000 * x is equal to 2000 - 100 * x\r<BR>\n" );
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document.write( "start with:<BR>\n" );
document.write( "6000 - 2000 * x = 2000 - 100 * x<BR>\n" );
document.write( "subtract 2000 from both sides of the equation and add 2000 * x to both sides of the equation to get:<BR>\n" );
document.write( "6000 - 2000 = 2000 * x - 100 * x<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "4000 = 1900 * x<BR>\n" );
document.write( "divide both sides of the eqution by 1900 to get:<BR>\n" );
document.write( "4000 / 1900 = x<BR>\n" );
document.write( "solve for x to get x = 4000 / 1900 = 2.105263158 hours.\r<BR>\n" );
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document.write( "they will both have the same number of cells in 2.105263158 hours.\r<BR>\n" );
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document.write( "in the first formula, you get f = 6000 - 2000 *  2.105263158 = 1789.473684\r<BR>\n" );
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document.write( "in the second formula, you get f = 2000 - 100 * 2.105263158 = 1789.473684\r<BR>\n" );
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document.write( "they both have the same number of cells in 2.105263158 hours.\r<BR>\n" );
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