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I think you are trying to create a formula for this set of data. There are two ways - (1) use a graphing utility and the list functions, (2) paper and pencil.
\n" ); document.write( "I will go through the paper pencil approach. \r
\n" ); document.write( "\n" ); document.write( "step 1: list the outputs: 2, 5, 9, 14, 20, 27, 35, 44.
\n" ); document.write( "step 2: take successive differences: 5-2 = 3, 9-5 = 4, 14-9 = 5, 20-14 = 6, 27-20 = 7, and so on. Notice this \"first level\" of successive differences is 3, 4, 5, 6, 7, 8, 9. They are all not the same.
\n" ); document.write( "step 3: take a \"second level\" of successive differences: we get 1, 1, 1, 1, 1, and so on. We have the first part of our equation at 1x^2 / 2!. The general rule for this is
\n" ); document.write( "[successive difference number] X ^(number of levels it took) / (number of levels!)
\n" ); document.write( "step 4: put in the numbers 1, 2, and 3 for x to get: 1/2, 4/2, 9/2.
\n" ); document.write( "step 5: subtract these from our first three outputs to get:
\n" ); document.write( "2-1/2 = 3/2, 5-4/2 = 6/2, 9-9/2 = 9/2
\n" ); document.write( "step 6: With the answers from step 5, take successive differences. we get 3/2, 3/2, 3/2. We have the second part of our equation at (3/2)X^1 / 1!.
\n" ); document.write( "Step 7: putting the information from step 3 and step 6 together, we get
\n" ); document.write( "x^2/2 + 3x/2. This is the equations that models your data set.\r
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