document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=979943>Question 979943</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Using the function, what happens to the intensity if you double the distance from the light<BR>\n" );
document.write( "source? (Consider a certain distance and use the function to determine the intensity. Then<BR>\n" );
document.write( "double the distance and determine the intensity. Do this for several pairs of distances. You<BR>\n" );
document.write( "should see a pattern develop. Express that pattern. Hint: you should be able to multiply<BR>\n" );
document.write( "the first intensity by some number and get the second intensity.) \r<BR>\n" );
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document.write( "Function: f(x) =800/x^2\r<BR>\n" );
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document.write( "Distance from sensor (cm)		20	30	40	50	60	70	80	90	100\r<BR>\n" );
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document.write( "Intensity Gauge Reading		1	.86	.48	.39	.27	.19	.16	.13	.03\r<BR>\n" );
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document.write( "I doubled the distance but I kept getting a differing pattern each time. Any help would be appreciated.	  <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 #601173 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=601173\">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( "Picking a number and then trying it, or even picking several numbers and trying them is an ok strategy to get an idea of what is happening, but it is a poor strategy for proving a mathematical relationship.  For this you need to choose an arbitrary value and operate on that abstract quantity.\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large x\"> represent the original distance, so <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 2x\"> must be the doubled distance. Compare <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(x)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(2x)\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f(x)\ =\ \frac{800}{x^2}\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f(2x)\ =\ \frac{800}{(2x)^2}\ =\ \frac{200}{x^2}\">\r<BR>\n" );
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document.write( "And therefore\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ f(2x)\ =\ \frac{1}{4}f(x)\">\r<BR>\n" );
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document.write( "Hence, for any physically possible distance value x, the intensity is divided by 4 when the distance is doubled.\r<BR>\n" );
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document.write( "Extra credit.  What happens to the intensity when the distance is multiplied by some number n?  In other words, compare <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(x)\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large f(nx)\"> \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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