document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=617719>Question 617719</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There is one homework question I am stuck on and cannot understand what I am doing wrong. We are worknig on graph shifts. The question is,<BR>\n" );
document.write( "At a certain vineyard it is found that each grape vine produces about 10 pounds of grapes in a season when about 800 vines are planted per acre. For each additional vine that is planted, the production of each vine decreases by about 1 percent. So the number of pounds of grapes produced per acre is modeled byA(n)=(800+n)(10-0.01n) where n is the number of additional vines planted Find the number of vines that should be planted to maximize grape production.\r<BR>\n" );
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document.write( "I have come up with A(n)= -0.01(n+100)^2+8100 and put in the answer of 100, 8100, 800 and many others and nothing is right. I don't understand what I am doing wrong. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #388523 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=388523\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your equation is:<BR>\n" );
document.write( "a(n) = (800 + n) * (10 - .01n)<BR>\n" );
document.write( "that doesn't look right.<BR>\n" );
document.write( "let's see how it works.<BR>\n" );
document.write( "if you don't plan an extra vine, then you will get:<BR>\n" );
document.write( "a(0) = (800) * (10) which would equal 8000 pounds per acre per season.<BR>\n" );
document.write( "if you add 1 vine to the acre, then your production is:<BR>\n" );
document.write( "a(1) = (801) * (10 - .01) which would then be equal to:<BR>\n" );
document.write( "a(1) = 801 * 9.99 which would be equal to 8001.99<BR>\n" );
document.write( "1 percent of 10 is equal to .01 * 10 which is equal to .1<BR>\n" );
document.write( "if you subtract .1 from 10, you get 9.9.<BR>\n" );
document.write( "your problem appears to be in your factor.<BR>\n" );
document.write( "the equation should be:<BR>\n" );
document.write( "a(n) = (800 + n) * (10 - .01*n*10) which would then be equal to:<BR>\n" );
document.write( "a(n) = (800 + n) * (10 - .1*n)<BR>\n" );
document.write( "that's where i think you went wrong.<BR>\n" );
document.write( "let's see if that straightens it out.<BR>\n" );
document.write( "a(0) = 800 * 10 = 8000 so that's ok.<BR>\n" );
document.write( "a(10) = (800 + 10) * (10 - .1*10) which is equal to:<BR>\n" );
document.write( "a(10) = (810) * (9) which is equal to 7290<BR>\n" );
document.write( "let's see if this makes sense.<BR>\n" );
document.write( "you add 10 vines to the acre and your yield decreases by 1 percent for each additional vine that's planted.<BR>\n" );
document.write( "if so, then your yield per vine should have decreased from 10 pounds to 9 pounds.<BR>\n" );
document.write( "that gets you 9 * 810 = 7290 pounds.<BR>\n" );
document.write( "i think the equation is now correct.<BR>\n" );
document.write( "check it out and let me know how you did.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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