document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=988799>Question 988799</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please help me with this problem?\r<BR>\n" );
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document.write( "Determine the average rate of change of the function between the given values of the variable.<BR>\n" );
document.write( "f(t)=7/t             \r<BR>\n" );
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document.write( " t=a, t=a+h\r<BR>\n" );
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document.write( "The formula confuses me and I'm not sure where to start. Can you help me solve this?\r<BR>\n" );
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document.write( "Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #609250 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=609250\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "The average rate of change of a function is defined as the slope of the secant line between two points of interest on the graph of the function.\r<BR>\n" );
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document.write( "If you select a point <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(t,f(t)\right)\"> on the function and then choose an amount of change in the independent variable of <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large h\">, then the new point will be <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(t+h,f(t+h)\right)\">.  The average rate of change will be the slope of the line that passes through these two points.\r<BR>\n" );
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document.write( "Recall the formula for the slope of a line:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ m\ =\ \frac{y_1\ -\ y_2}{x_1\ -\ x_2} \">\r<BR>\n" );
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document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(x_1,y_1\right)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \left(x_2,y_2\right)\"> are the coordinates of the given points.\r<BR>\n" );
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document.write( "Compare this to the average rate of change formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\text{\Delta}{y}}{\text{\Delta}{x}}\ =\ \frac{f(x\ +\ h)\ -\ f(x)}{(x\ +\ h)\ -\ x}\ =\ \frac{f(x\ +\ h)\ -\ f(x)}{h}\">\r<BR>\n" );
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document.write( "See illustration\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=solver91311&illustration_name=AverageRateOfChange.jpg\">.\r<BR>\n" );
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document.write( "For your given function, just plug into the formula:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \frac{\frac{7}{t\ +\ h}\ -\ \frac{7}{t}}{h}\ =\ \frac{\frac{7t\ -\ 7(t\ +\ h)}{t^2\ +\ th}}{h}\ =\ \frac{-7}{t^2\ +\ th}\">\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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