Difference between revisions of "Derivation of developer productivity decline function"

Revision as of 19:16, 27 August 2020

Derivation of developer productivity decline function

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-The first assumption is that developer productivity declines with a constant rate <math>r</math>:
+Derivation of developer productivity decline function
-(1) <math>\frac{dP(t)}{dt}</math> = <math>-r \cdot P(t)</math>
-Divide by <math>P(t)</math>:
-(2) <math>\frac{1}{P(t)}</math> <math>\cdot</math> <math>\frac{dP(t)}{dt}</math> = <math>-r</math>
-(3) <math>\frac{dP(t)}{P(t)}</math> = <math>-r dt</math>
-(4) <math>\int \frac{dP(t)}{P(t)}</math> = <math>-r \int t dt</math>
-(5) <math>ln(P(t))= -rt +C </math>
-Exponantiate both sides:
-(6) <math>P(t) = e^{-rt}e^C </math>
-(7) <math>P(t) = e^C \cdot e^{-rt} =e^C \cdot 1</math>
-As P(0) = P_0 we get:
-(8) <math>P(0) = e^C \cdot e^{-r \cdot 0} = e^C \cdot 1</math>
-So <math>P(0) = e^C</math> giving:
-(9) <math>P(t) = P_0 \cdot e^{-rt}</math>
-See: http://en.wikipedia.org/wiki/Exponential_decay#Solution_of_the_differential_equation
 [[Category:math]]