document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=153160>Question 153160</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi\r<BR>\n" );
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document.write( "How would I solve the following: Exponent and logarithm as function of power\r<BR>\n" );
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document.write( "True or false: The function \"f(x) = 3x\" grows three times faster than the function \"g(x) = x\".  Explain.  I got two different answer when I tried to solve this logarithm. Can you please help me.\r<BR>\n" );
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document.write( "Answer: False.<BR>\n" );
document.write( "If x = 3 it would make f(3)=3 * 3 =9 and g(3)=3<BR>\n" );
document.write( "If x = 4 then f(4)=12 and g(4)=4<BR>\n" );
document.write( "if x=5 then f(5)=15 and g(5)=5\r<BR>\n" );
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document.write( "although f(x) is 3 times greater than g(x) the growth of f(x) is not 3 times faster than g(x) because from 9 the change of f(x) is only 3 and from 12 it only changed by 3 again. wherein it should have incurred a change of 9. If f(x) grows three times faster than g(x) the equation should be f(x)=x raise to the 3rd power and g(x)=x.\r<BR>\n" );
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document.write( "Answer is True<BR>\n" );
document.write( "The question is on rate of growth, ie slope.\r<BR>\n" );
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document.write( "slope of g(x) is 1. <BR>\n" );
document.write( "slope of f(x) is 3.<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 #112695 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=112695\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1st: This is not a logarithm problem<BR>\n" );
document.write( "2nd: When you say \" it should have grown by 9 \" you are<BR>\n" );
document.write( "pointing to the fact that when x increased from 0 to 3 <BR>\n" );
document.write( "f(x) increased from 0 to 9.<BR>\n" );
document.write( "That is true.<BR>\n" );
document.write( "But, if x had increased from 0 to 1 f(x) would have increased<BR>\n" );
document.write( "by only 3.  Similarly for x increasing from 1 to 2, then from<BR>\n" );
document.write( "2, to 3.  So for each increase in x by one f(x) increases by 3.<BR>\n" );
document.write( "That is a description of the slope; and the slope is the rate<BR>\n" );
document.write( "of growth for a linear function.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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