document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=188742>Question 188742</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm having difficulty understanding this problem...<BR>\n" );
document.write( "I am asked to evaluate the functions for the values of x given as 1,2,4,8 and 16. Describe the differences in the rate at which each function changes with increasing values of x:\r<BR>\n" );
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document.write( "if the functions are<BR>\n" );
document.write( "f(x) = x^2 - 4x + 3 which is a quadratic function producing the points<BR>\n" );
document.write( "(1,0)(2,-1),(4,3),(8,35),(16,195)\r<BR>\n" );
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document.write( "f(x) = 7^x which is an exponential function producing the points<BR>\n" );
document.write( "(1,7)(2,49),(4,2401),(8,5764801), and (16,3.323X10^13)\r<BR>\n" );
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document.write( "f(x) = log x which is a logarithmic function producing the points<BR>\n" );
document.write( "(1,0), (2,0.3), (4, 0.6), (8, 0.9)and (16, 1,2)\r<BR>\n" );
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document.write( "I am sure that the quadratic function is much more accelerated in rate than a linear function, and the exponential function is the fastest rate of all, with the slowest rate by the logarithmic function. But I am not sure how to justify each evaluation of rate? Could you please help me understand how to arrive at evaluating the differences in rate of these functions? Thanks!\r<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 #141571 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=141571\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You might do this.  Pick the 1st and last point for each of<BR>\n" );
document.write( "your examples. Find the slope for each of those cases.  That<BR>\n" );
document.write( "will give you the average slope over the interval.  Compare<BR>\n" );
document.write( "those averages.<BR>\n" );
document.write( "You could also find the slope between each pair of points<BR>\n" );
document.write( "and draw your conclusion.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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