document.write( "Question 189524This question is from textbook Algebra 2
\n" ); document.write( ": I really need your help in writing an exponential function whose graph passes through the points (0,-5) and (-2,-20). Then determining whether the function represents exponential growth or decay. I would really appreciate any help! \n" ); document.write( "
Algebra.Com's Answer #142218 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
Edwin's solution:\r
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document.write( "It has to be growth because when x goes from a smaller value -2\r\n" );
document.write( "to larger value 0, y also grows from a smaller value -20 to a \r\n" );
document.write( "larger value -5.  That is a growth.\r\n" );
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document.write( "We start with the basic exponential equation:\r\n" );
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document.write( "\"y+=+A%2AB%5Ex\"\r\n" );
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document.write( "Then we substitute the point (0,-5)\r\n" );
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document.write( "\"y+=+A%2AB%5Ex\"\r\n" );
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document.write( "\"-5+=+A%2AB%5E0\"\r\n" );
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document.write( "\"-5+=+A%2A1\"\r\n" );
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document.write( "\"-5+=+A+\"\r\n" );
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document.write( "So the exponential equation \"y+=+A%2AB%5Ex\" is now\r\n" );
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document.write( "\"y+=+-5%2AB%5Ex\"\r\n" );
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document.write( "Now we substitute the other point (-2, -20)\r\n" );
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document.write( "\"-20+=+-5%2AB%5E%28-2%29\"\r\n" );
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document.write( "And simplify:\r\n" );
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document.write( "\"-20+=+-5%2A%281%2FB%5E2%29\"\r\n" );
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document.write( "Multiply both sides by \"B%5E2\"\r\n" );
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document.write( "\"-20B%5E2+=+-5\"\r\n" );
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document.write( "Divide both sides by -20\r\n" );
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document.write( "\"B%5E2+=+%28-5%29%2F%28-20%29\"\r\n" );
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document.write( "\"B%5E2+=+1%2F4\"\r\n" );
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document.write( "\"B+=+sqrt%281%2F4%29\"\r\n" );
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document.write( "\"B+=+1%2F2\"\r\n" );
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document.write( "So the equation \"y+=+-5%2AB%5Ex\" is now\r\n" );
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document.write( "\"y+=+-5%2A%281%2F2%29%5Ex\"\r\n" );
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document.write( "The graph looks like this:\r\n" );
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document.write( "\"graph%28200%2C100%2C-3%2C3%2C-40%2C10%2C-5%2A%28.5%29%5Ex%29\"\r\n" );
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document.write( "which shows it's a growth.\r\n" );
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document.write( "Edwin
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