document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1138238>Question 1138238</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone please help? I’m completely confused on how to solve the equation:<BR>\n" );
document.write( "Find the exponential function that passes through the points. \r<BR>\n" );
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document.write( "x: 1, 2, 3, 4 \r<BR>\n" );
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document.write( "h(x): 40,  16,   6.4,  2.56 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #756079 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=756079\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> here's what i get.\r<BR>\n" );
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document.write( "general form for exponential function is y = ab^x.\r<BR>\n" );
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document.write( "when x = 1, you get ab^1 = 40<BR>\n" );
document.write( "when x = 2, you get ab^2 = 16<BR>\n" );
document.write( "when x = 3, you get ab^3 = 6.4<BR>\n" );
document.write( "when x = 4, you get ab^4 = 2.56\r<BR>\n" );
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document.write( "if you take ab^2 and divide it by ab^1, you get .4<BR>\n" );
document.write( "if you take ab^3 and divide it by ab^2, you get .4<BR>\n" );
document.write( "if you take ab^4 and divide it by ab^3, you get .4\r<BR>\n" );
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document.write( "take a look at any one of these and you'll see that a drops out of the equation each time.\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "ab^4 / ab^3 = 2.56 / 6.4 = .4\r<BR>\n" );
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document.write( "this results in ab^4 / ab^3 = .4\r<BR>\n" );
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document.write( "the a in the numerator and the a in the denominator cancel out and you are left with b^4 / b^3 = .4\r<BR>\n" );
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document.write( "since b^4 / b^3 is equal to b^(4-3), you are left with b = .4\r<BR>\n" );
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document.write( "therefore, your equations become:\r<BR>\n" );
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document.write( "a * .4^1 = 40<BR>\n" );
document.write( "a * .4^2 = 16<BR>\n" );
document.write( "a * .4^3 = 6.4<BR>\n" );
document.write( "a * .4^4 = 2.56\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "a * .4 = 40 which means a = 100.<BR>\n" );
document.write( "a * .4^2 = 16 becomes a * .16 = 16 which means a = 100<BR>\n" );
document.write( "go down the line and a will be 100 each time.\r<BR>\n" );
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document.write( "your exponential equation in the form of ab^x becomes 100 * .4^x.\r<BR>\n" );
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document.write( "you can graph this function as shown below.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2019/040421.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the graph shows that the solution is correct.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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