document.write( "Question 1190085: Write an exponential function in the form y=ab^x
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Algebra.Com's Answer #821644 by ikleyn(52800) $\"\"$ $\"About$

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\n" ); document.write( "Write an exponential function in the form y=ab^x
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document.write( "In this problem, it is assumed that the parameter b is a positive real number.\r\n" );
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document.write( "First, the problem says that the plot of the function goes through point (0,12).\r\n" );
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document.write( "It means that the value of the function is 12 at x= 0.\r\n" );
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document.write( "So we write  12 = ,  but since   = 1 for any admittable value of b,\r\n" );
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document.write( "it implies that  a = 12.\r\n" );
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document.write( "Hence, we can write the function in the form  y = .\r\n" );
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document.write( "Next, the problem says that the plot of the function goes through point (2,768).\r\n" );
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document.write( "It means that the value of the function is 768 at x= 2.\r\n" );
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document.write( "So we write  768 = .\r\n" );
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document.write( "Dividing both sides by 12, we get   =  = 64.\r\n" );
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document.write( "It implies that  b =  = 8  (we accept positive value of the square root, only).\r\n" );
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document.write( "Finally, the function is  y = .\r\n" );
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document.write( "You may check, that this function satisfies the imposed conditions.\r\n" );
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