document.write( "Question 406573: write an exponential function that includes (2,20)(0,5) \n" ); document.write( "

Algebra.Com's Answer #286831 by richard1234(7193) $\"\"$ $\"About$

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Suppose our exponential function is in the form\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29+=+ab%5Ex\"$ , where a and b are nonzero constants. Since f(0) = 5, then\r
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\n" ); document.write( "\n" ); document.write( " $\"5+=+ab%5E0\"$ --> a = 5.\r
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\n" ); document.write( "\n" ); document.write( "Also, since f(2) = 20, we can substitute and get $\"20+=+5%2A%28b%5E2%29\"$ --> b = 2 (the solution b = -2 is somewhat extraneous because it's not easily defined on real numbers, and not exponential). Therefore we can write $\"f%28x%29+=+5%2A2%5Ex\"$ . \n" ); document.write( "

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