document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=277935>Question 277935</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2.	Biologists want to set up a station to test alligators in the lake for West Nile Virus. Suppose that the costs for such a station are $2,500 for setup costs and $3.00 to administer each test. \r<BR>\n" );
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document.write( "a.	Write an expression that gives the total cost to test x animals.\r<BR>\n" );
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document.write( "b.	You can find the average cost per animal by dividing total costs by number of animals. Write the expression that gives the average cost per animal.\r<BR>\n" );
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document.write( "c.	Find the average cost per animal for 10 animals, 100 animals, and 1,000 animals.\r<BR>\n" );
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document.write( "d.	As the number of animals tested increases, what happens to the average cost to test the animals? Would the average cost ever fall below $3.00? If so, identify a value that supports your answer. If not, explain how you know. \r<BR>\n" );
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document.write( "e.	How many animals should be tested for the average cost to be $5.00 per animal? <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 #202308 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=202308\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> problem a:\r<BR>\n" );
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document.write( "c = 3*x + 2500\r<BR>\n" );
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document.write( "c is the total cost for setting up the station and administering the tests.\r<BR>\n" );
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document.write( "problem b:\r<BR>\n" );
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document.write( "a = (3*x+2500)/x\r<BR>\n" );
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document.write( "a is the average cost to test each animal.\r<BR>\n" );
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document.write( "that's the total cost divided by the number of animals tested.\r<BR>\n" );
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document.write( "problem c:\r<BR>\n" );
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document.write( "average cost for 10 animals is (3*10 + 2500)/10 = 2530/10 = $253.00\r<BR>\n" );
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document.write( "average cost for 100 animals is (3*100) + 2500)/100 = 2800/10 = $28.00\r<BR>\n" );
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document.write( "average cost for 1000 animals is (3*1000) + 2500)/1000 = 5500/1000 = $5.50\r<BR>\n" );
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document.write( "problem d:\r<BR>\n" );
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document.write( "average cost per animal goes down.\r<BR>\n" );
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document.write( "it will never go below $3.00 per animal.\r<BR>\n" );
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document.write( "as x gets larger, the percentage of 2500 / x gets smaller.\r<BR>\n" );
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document.write( "it can approach 0 but it will never be 0.\r<BR>\n" );
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document.write( "if it was 0, the average cost would be (3*x)/3 = $3.00\r<BR>\n" );
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document.write( "anything above that makes the average cost just a little bit higher than $3.00, but never below that.\r<BR>\n" );
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document.write( "example:\r<BR>\n" );
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document.write( "(3*(1 billion) + 2500)/1 billion equals:\r<BR>\n" );
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document.write( "3*(1 billion)/1 billion + 2500/(1 billion) which equals:\r<BR>\n" );
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document.write( "3 + (2500/(1 billion).\r<BR>\n" );
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document.write( "now 2500 / 1 billion is a very small number, but it is not equal to 0, so the average cost is going to be $3.00 + a very small number.\r<BR>\n" );
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document.write( "problem e:\r<BR>\n" );
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document.write( "the formula for average is:\r<BR>\n" );
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document.write( "a = (3*x + 2500)/x\r<BR>\n" );
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document.write( "set a = 5 and this formula becomes:\r<BR>\n" );
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document.write( "5 = (3*x + 2500)/x\r<BR>\n" );
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document.write( "multiply both sides of this equation by x to get:\r<BR>\n" );
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document.write( "5*x = 3*x + 2500\r<BR>\n" );
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document.write( "subtract 3*x from both sides of this equation to get:\r<BR>\n" );
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document.write( "2*x = 2500\r<BR>\n" );
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document.write( "divide both sides of this equation by 2 to get:\r<BR>\n" );
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document.write( "x = 1250\r<BR>\n" );
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document.write( "at 1250 tests, the average cost should be $5.00 per test.\r<BR>\n" );
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document.write( "plug this into the original equation for average to see if it holds.\r<BR>\n" );
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document.write( "a = (3*x + 2500)/x becomes:\r<BR>\n" );
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document.write( "a = (3*1250 + 2500) / 1250 which becomes:\r<BR>\n" );
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document.write( "a = 3750 + 2500) / 1250 which becomes:\r<BR>\n" );
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document.write( "a = 6250 / 1250 which becomes:\r<BR>\n" );
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document.write( "a = 5\r<BR>\n" );
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document.write( "the average cost per test of $5.00 is confirmed to be true.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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