document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187399>Question 1187399</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The number of bacteria in a refrigerated food product is given by  \r<BR>\n" );
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document.write( "N(T)=24T2-108T+68,  4<T<34 where T is the temperature of the food. <BR>\n" );
document.write( "When the food is removed from the refrigerator, the temperature is given by  <BR>\n" );
document.write( "T(t)=9t+1.3, where t is the time in hours.\r<BR>\n" );
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document.write( "Find the composite function  <BR>\n" );
document.write( "N(T(t))=1944t2−410.4t−31.84. Correct <BR>\n" );
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document.write( "Find the number of bacteria after 3.2 hours. Give your answer accurate to the nearest whole value.<BR>\n" );
document.write( "  ?   bacteria\r<BR>\n" );
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document.write( "The first part I got it correct I only need help with the secont part pleas. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #818387 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=818387\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> here's how it works, i believe.\r<BR>\n" );
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document.write( "you are given that t = 3.2.\r<BR>\n" );
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document.write( "solve for T(t) to get:\r<BR>\n" );
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document.write( "T(t) = 9t + 1.3 = 9*3.2 + 1.3 = 30.1\r<BR>\n" );
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document.write( "that's the value of T.\r<BR>\n" );
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document.write( "go back to your original equation and replace T with 30.1.\r<BR>\n" );
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document.write( "you will get:\r<BR>\n" );
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document.write( "N(T)=24T2-108T+68 becomes:\r<BR>\n" );
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document.write( "N(T) = 24 * 30.1^2 - 108 * 30.1 + 68 = 18561.44.\r<BR>\n" );
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document.write( "now go back to your composite function and replace t with 3.2 to get:\r<BR>\n" );
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document.write( "N(T(t))=1944t2−410.4t−31.84 becomes:\r<BR>\n" );
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document.write( "N(T(t)) = 1944 * 3.2^2 - 410.4 * 3.2 1 31.84 = 18561.44\r<BR>\n" );
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document.write( "the answer is exactly the same.\r<BR>\n" );
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document.write( "it should be right on because the composite function is the same as solving for T(t) first and then using the result of that as input to N(T).\r<BR>\n" );
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document.write( "that's what composite functions do.\r<BR>\n" );
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document.write( "they combine the operations of 2 equations into 1 equation.<BR>\n" );
document.write( "you used T(t) to get T.<BR>\n" );
document.write( "you then place T in the equation of N(T) to get N.\r<BR>\n" );
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document.write( "i'll give you a simpler example.\r<BR>\n" );
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document.write( "f(x) = x^2<BR>\n" );
document.write( "g(x) = (x-1)<BR>\n" );
document.write( "f(g(x)) = (x-1)^2 = x^2 - 2x + 1\r<BR>\n" );
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document.write( "if x = 5, then f(5) = 5^2 = 25 and g(x) = 4.\r<BR>\n" );
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document.write( "f(g(x)) = (5-1)^2 = 4^2 = 16\r<BR>\n" );
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document.write( "when you solve g(x) first, you get x = 4.<BR>\n" );
document.write( "you then solve for f(g(x)) = f(4) = 4^2 = 16.\r<BR>\n" );
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document.write( "the composite function is the same as first solving for the inner function and then using the value from the inner function to solve for the outer function.\r<BR>\n" );
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document.write( "T(t) was the inner function.<BR>\n" );
document.write( "N(T) was the outer function.\r<BR>\n" );
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document.write( "here's a reference on composite functions.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.mathsisfun.com/sets/functions-composition.html\" target = \"_blank\">https://www.mathsisfun.com/sets/functions-composition.html</a>\r<BR>\n" );
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document.write( "let me know if you have any questions.\r<BR>\n" );
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document.write( "theo\r<BR>\n" );
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document.write( "good job on finding the composite function, by the way.\r<BR>\n" );
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document.write( "fyi, i messed up the original calculations because i wrote the equation down wrong.<BR>\n" );
document.write( "i have since corrected it.<BR>\n" );
document.write( "this is the corrected version.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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