document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=481250>Question 481250</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi thank you for your time! Here is the problem I am working on. WIll you show me how you come up with your solutions? Thank you again so much for your time!\r<BR>\n" );
document.write( "\n" );
document.write( "The world consumption of oil in millions of barrels per day is given by<BR>\n" );
document.write( "f(x)=-0.1x^2 + 2x + 58, where x is the number of years since 1985 (x=0 for 1985)\r<BR>\n" );
document.write( "\n" );
document.write( "a. According to this equation, what was the oil consumption in 1990?<BR>\n" );
document.write( "b. Using this equation, the maximum oil consumption will occur in what year?<BR>\n" );
document.write( "c. What is the maximum oil consumption?<BR>\n" );
document.write( "d. Does this equation realistically describe oil in 2030? why or why not?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #329534 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=329534\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x)=-0.1x^2 + 2x + 58, where x is the number of years since 1985 (x=0 for 1985)<BR>\n" );
document.write( "a. According to this equation, what was the oil consumption in 1990?<BR>\n" );
document.write( "1990 - 1985 = 5<BR>\n" );
document.write( "set x = 5 and solve f(5)<BR>\n" );
document.write( "f(x)=-0.1x^2 + 2x + 58<BR>\n" );
document.write( "f(5)=-0.1(5)^2 + 2(5) + 58<BR>\n" );
document.write( "f(5)=-0.1(25) + 10 + 58<BR>\n" );
document.write( "f(5)= 65.5 million barrels<BR>\n" );
document.write( ".<BR>\n" );
document.write( "b. Using this equation, the maximum oil consumption will occur in what year?<BR>\n" );
document.write( "It would be the vertex.<BR>\n" );
document.write( "x = -b/(2a)<BR>\n" );
document.write( "x = -2/(2(-0.1))<BR>\n" );
document.write( "x = -2/(-0.2)<BR>\n" );
document.write( "x = 10<BR>\n" );
document.write( "year:<BR>\n" );
document.write( "1985 + 10 = 1995<BR>\n" );
document.write( ".<BR>\n" );
document.write( "c. What is the maximum oil consumption?<BR>\n" );
document.write( "set x = 10 solve for f(x)<BR>\n" );
document.write( "f(x)=-0.1x^2 + 2x + 58<BR>\n" );
document.write( "f(5)=-0.1(10)^2 + 2(10) + 58<BR>\n" );
document.write( "f(5)=-0.1(100) + 20 + 58<BR>\n" );
document.write( "f(5)= 68 million barrels<BR>\n" );
document.write( ".<BR>\n" );
document.write( "d. Does this equation realistically describe oil in 2030? why or why not?<BR>\n" );
document.write( "2030-1985 = 45<BR>\n" );
document.write( "set x = 45 solve for f(x)<BR>\n" );
document.write( "f(x)=-0.1x^2 + 2x + 58<BR>\n" );
document.write( "f(5)=-0.1(45)^2 + 2(45) + 58<BR>\n" );
document.write( "f(5)=-0.1(2025) + 90 + 58<BR>\n" );
document.write( "f(5)=-54.5 million barrels<BR>\n" );
document.write( "answer: NO, because the result is negative<BR>\n" );
document.write( ".\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );