document.write( "Question 1180766: Determine a possible equation of a exponential function that satisfy the following properties. Include a sketch of the function in your solution. \r
\n" ); document.write( "\n" ); document.write( "a) Its y-intercept is 2\r
\n" ); document.write( "\n" ); document.write( "b) It has a horizontal asymptote at y = 5\r
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Algebra.Com's Answer #810544 by ikleyn(52802) $\"\"$ $\"About$

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\n" ); document.write( "Determine a possible equation of a exponential function that $\"highlight%28cross%28satisfy%29%29\"$ satisfies the following properties.
\n" ); document.write( "Include a sketch of the function in your solution.
\n" ); document.write( "a) Its y-intercept is 2
\n" ); document.write( "b) It has a horizontal asymptote at y = 5
\n" ); document.write( "c) it is always increasing
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document.write( "y = ab^(-x) + c\r\n" );
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document.write( "Coefficient \"a\" must be negative (I will take it in the form  a = - A,  where A is positive).\r\n" );
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document.write( "The base \"b\" must be positive, and can be any positive number; I will take b = 2.\r\n" );
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document.write( "Coefficient \"c\" must be equal to 5.\r\n" );
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document.write( "     y = -Ab^(-x) + 5.\r\n" );
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document.write( "An additional condition is  -Ab^0 + 5 = 2,  which gives  A = 5 - 2 = 3.\r\n" );
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document.write( "Final function  y = -3*2^(-x) + 5.     ANSWER\r\n" );
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document.write( "                       Visual check\r\n" );
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document.write( "    \r\n" );
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document.write( "          Plot y = -3*2^(-x) + 5 (red)  and  y = 5  (green)\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved and checked.\r
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\n" ); document.write( "\n" ); document.write( "It is one of many possible examples. There are many (infinitely many) other functions with similar properties.\r
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