document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=600584>Question 600584</A>: <I><SPAN STYLE=\"word-break: break-all;\"> which grows faster as x increases, x^3 of 3^x? Explain with examples. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #379393 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=379393\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 3^x grows faster because from x = 4 to x = 5, we get the following\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x = 4:\r<BR>\n" );
document.write( "\n" );
document.write( "x^3 = 4^3 = 64\r<BR>\n" );
document.write( "\n" );
document.write( "3^x = 3^4 = 81\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "---------------------\r<BR>\n" );
document.write( "\n" );
document.write( "x = 5\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "x^3 = 5^3 = 125\r<BR>\n" );
document.write( "\n" );
document.write( "3^x = 3^5 = 243\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So as x goes from 4 to 5, x^3 goes from 64 to 125. At the same time, 3^x goes from 81 to 243. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Subtract each result:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For x^3: 125 - 64 = 61\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "For 3^x: 243 - 125 = 118\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "and you can see that the change from x = 4 to x = 5 is much larger for 3^x\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This shows us that 3^x grows faster as x increases. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );