The standard inverse sigmoid function, (1/(1+e^x)), multiplied by 'M', to increase the height, shifted by 'M' to make the maximum bonus at 0 hours, and a multiplier of '10/a' on x to stretch the graph lengthwise.
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Expression 6: "f" left parenthesis, "x" , right parenthesis equals StartFraction, "M" Over 1 plus "e" Superscript, left parenthesis, StartNestedFraction, 10 "x" NestedOver "a" , EndNestedFraction minus "M" , right parenthesis , Baseline , EndFractionfx=M1+e10xa−M
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The sigmoid function rounded to the whole numbers. Click the circle on the left to show/hide.
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Expression 8: "f" left parenthesis, "x" , right parenthesis equals round left parenthesis, StartFraction, "M" Over 1 plus "e" Superscript, left parenthesis, StartNestedFraction, 10 "x" NestedOver "a" , EndNestedFraction minus "M" , right parenthesis , Baseline , EndFraction , right parenthesisfx=roundM1+e10xa−M