document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172722>Question 1172722</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Current annual consumption of energy is 78 billion units, and this is expected to rise at a fixed rate of 5.8% each year. The capacity of the industry to supply energy is currently 104 billion units.<BR>\n" );
document.write( "(a) Assuming that the supply remains steady, after how many years will demand exceed supply?<BR>\n" );
document.write( "(b) What constant rate of growth of energy production would be needed to satisfy demand for the next 50 years? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #797835 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=797835\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 78(1.058)^t=104<BR>\n" );
document.write( "1.058^t=1.333<BR>\n" );
document.write( "t ln 1.058=ln 1.333<BR>\n" );
document.write( "t=ln (1.333)/ln (1.058)<BR>\n" );
document.write( "=5.098 years<BR>\n" );
document.write( "-<BR>\n" );
document.write( "78*1.058^50=1307.31 billion units<BR>\n" );
document.write( "104*(1+r)^50=1307.31<BR>\n" );
document.write( "(1+r)^50=12.570<BR>\n" );
document.write( "50 ln(1+r)=ln 12.570;<BR>\n" );
document.write( "ln(1+r)=2.5313/50=0.0506<BR>\n" );
document.write( "raise to e power<BR>\n" );
document.write( "1+r=1.05193<BR>\n" );
document.write( "r=5.193%<BR>\n" );
document.write( "round at end, not intermediate calculations<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );