document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=91088>Question 91088</A>: <I><SPAN STYLE=\"word-break: break-all;\"> this is possibly the harderst proble I have ever seen in my life. Please help me. I have such a difficult time with word problems.  Please help me with this so I can get on with the rest of my math. I really appreciate your help\r<BR>\n" );
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document.write( "This problem set involves a formula (a rational function) with which a new tortilla company might be able to forecast its production over the first few weeks of operation. <BR>\n" );
document.write( "In this formula, C(t) is the number of bags of tortillas that can be produced per week after t weeks of production. <BR>\n" );
document.write( "Here is the rational function that was developed to best describe the fledgling company's production.<BR>\n" );
document.write( "c (t)= 1000t^2 -10,000t / t^2-10t+25 <BR>\n" );
document.write( "What does the graph of the function look like? To answer this question, find<BR>\n" );
document.write( "a. The vertical asymptotes, if any: <BR>\n" );
document.write( "b. The horizontal asymptote, if any: <BR>\n" );
document.write( "c. The t intercepts, if any: <BR>\n" );
document.write( "d. The C intercept, if any: <BR>\n" );
document.write( "e. The value of C(t) at: <BR>\n" );
document.write( "t = 10 weeks<BR>\n" );
document.write( "t = 15 weeks<BR>\n" );
document.write( "t = 20 weeks<BR>\n" );
document.write( "t = 25 weeks<BR>\n" );
document.write( "t = 30 weeks<BR>\n" );
document.write( "t = 35 weeks<BR>\n" );
document.write( "Show your calculations <BR>\n" );
document.write( "f. The value of C(t) at:<BR>\n" );
document.write( "t = -5<BR>\n" );
document.write( "t = -10 <BR>\n" );
document.write( "What is the projected maximum number of bags of tortillas that the company can never exceed? Discuss this answer in terms of the horizontal asymptote. <BR>\n" );
document.write( "3. Can the company reach that maximum? If so, after how long <BR>\n" );
document.write( "4. Give an interpretation of what might be happening to the company's production efforts from week 5 to week 10? Discuss this answer in detail. <BR>\n" );
document.write( "5. In terms of the business application, is there any meaning for the value of C(t) when t = -5 and t = -10? Explain your answer. \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 #66109 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=66109\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> C(t) is the number of bags of tortillas that can be produced per week after t weeks of production. <BR>\n" );
document.write( "Here is the rational function that was developed to best describe the fledgling company's production.<BR>\n" );
document.write( "c (t)= 1000t^2 -10,000t / t^2-10t+25 <BR>\n" );
document.write( "What does the graph of the function look like?<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "To answer this question, find<BR>\n" );
document.write( "a. The vertical asymptotes: t=5<BR>\n" );
document.write( "--------------------<BR>\n" );
document.write( "b. The horizontal asymptote:t = 1000<BR>\n" );
document.write( "----------------------<BR>\n" );
document.write( "c. The t intercepts, if any:<BR>\n" );
document.write( "Let C(t) = 0; solve for t as follows:<BR>\n" );
document.write( "1000t^2-10000t = 0<BR>\n" );
document.write( "1000t(t-10) = 0<BR>\n" );
document.write( "t-intercepts at t=0 and at t=10<BR>\n" );
document.write( " -------------------------<BR>\n" );
document.write( "d. The C intercept, if any:<BR>\n" );
document.write( "Let t=0 then C(0)=0<BR>\n" );
document.write( "--------------------------<BR>\n" );
document.write( "I'll leave the following to you. <BR>\n" );
document.write( "e. The value of C(t) at: <BR>\n" );
document.write( "t = 10 weeks<BR>\n" );
document.write( "t = 15 weeks<BR>\n" );
document.write( "t = 20 weeks<BR>\n" );
document.write( "t = 25 weeks<BR>\n" );
document.write( "t = 30 weeks<BR>\n" );
document.write( "t = 35 weeks<BR>\n" );
document.write( "Show your calculations <BR>\n" );
document.write( "f. The value of C(t) at:<BR>\n" );
document.write( "t = -5<BR>\n" );
document.write( "t = -10 <BR>\n" );
document.write( "What is the projected maximum number of bags of tortillas that the company can never exceed? Discuss this answer in terms of the horizontal asymptote.<BR>\n" );
document.write( "C(t) can never reach or exceed 1000<BR>\n" );
document.write( "------------------------ <BR>\n" );
document.write( "3. Can the company reach that maximum? If so, after how long <BR>\n" );
document.write( "No, 1000 is an asymtotic value; C(t) is always < 1000<BR>\n" );
document.write( "------------------------<BR>\n" );
document.write( "4. Give an interpretation of what might be happening to the company's production efforts from week 5 to week 10? Discuss this answer in detail.<BR>\n" );
document.write( "During that interval C(t)<0 but increasing.<BR>\n" );
document.write( "------------------- <BR>\n" );
document.write( "5. In terms of the business application, is there any meaning for the value of C(t) when t = -5 and t = -10? Explain your answer.<BR>\n" );
document.write( "It might model the production before t=0; or it might be meaningless<BR>\n" );
document.write( "if the company did not exist during those weeks.<BR>\n" );
document.write( "=======================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " \r<BR>\n" );
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