document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1168699>Question 1168699</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If f(x)=7^x , then f(x+3)-f(x+1) equals:\r<BR>\n" );
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document.write( "A) 2f(x)<BR>\n" );
document.write( "B) 336f(x)<BR>\n" );
document.write( "C) 342f(x)<BR>\n" );
document.write( "D) 343<BR>\n" );
document.write( "E) 2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #793288 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=793288\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> f(x) = 7^x<BR>\n" );
document.write( "f(x+3) = 7^(x+3)<BR>\n" );
document.write( "f(x+1) = 7^(x+1)\r<BR>\n" );
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document.write( "f(x+3) - f(x+1) = 7^(x+3) - 7^(x+1)\r<BR>\n" );
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document.write( "f(x+3) = 7^(x+3) = 7^3 * 7^x<BR>\n" );
document.write( "f(x+1) = 7^(x+1) = 7^1 * 7^x<BR>\n" );
document.write( "f(x+3) - f(x+1) = 7^3 * 7^x - 7^1 * 7^x<BR>\n" );
document.write( "factor out 7^x to get:<BR>\n" );
document.write( "f(x+3) - f(x+1) = (7^3 - 7^1) * 7^x<BR>\n" );
document.write( "this becomes f(x+3) - f(x+1) = 336 * 7^x<BR>\n" );
document.write( "since 7^x = f(x), you get f(x+3) - f(x+1) = 336 * f(x).\r<BR>\n" );
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document.write( "that would be selection B.\r<BR>\n" );
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document.write( "what it says is that f(x+3) - f(x+1) is equivalent to 336 * f(x).\r<BR>\n" );
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document.write( "these two expressions can be made equal to y and graphed to show that they make identical graphs.\r<BR>\n" );
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document.write( "your two equations to graph are:\r<BR>\n" );
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document.write( "y = 7^(x+3) - 7^(x+1) and y = 336*7^x\r<BR>\n" );
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document.write( "you will see that, on the graph, these these two equations make the same graph. in other words, the graphs are identical because the equations are equivalent.\r<BR>\n" );
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document.write( "here's the graph.<BR>\n" );
document.write( "the graph of each equation is in red.<BR>\n" );
document.write( "you only see one curve, because the graphs are identical.\r<BR>\n" );
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document.write( "if you were to calculate both equations for x = 0 to 5, you would get:\r<BR>\n" );
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document.write( "x               y = 336*7^x                      y=7^(x+3) - 7^(x+1)\r\n" );
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document.write( "0               336*7^0 = 336                    7^3 - 7^1 = 336\r\n" );
document.write( "1               336*7^1 = 2,352                  7^4 - 7^2 = 2,352\r\n" );
document.write( "2               336*7^2 = 16,464                 7^5 - 7^3 = 16,464\r\n" );
document.write( "3               336*7^3 = 115,248                7^6 - 7^4 = 115,248\r\n" );
document.write( "4               336*7^4 = 806,736                7^7 - 7^5 = 806,736\r\n" );
document.write( "5               336*7^5 = 5,647,152              7^8 - 7^6 = 5,647,152\r\n" );
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document.write( "</PRE>\r<BR>\n" );
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