# Thread: little engineering/little calc

1. ## little engineering/little calc

In dealing with metal surfaces that undergo oxidation, the thickness of the oxide film has been found to increase exponentially with time, such that d=dmax (1-e^(-kt)), t>2000 where d=thickness of oxide film and t=time.
This expression is the result of integrating an ordinary differential equation.

I'm trying to derive the Ordinary differential equation and the associated initial condition needed that produces d=dmax (1-e^(-kt))

Any help for how to approach this is much appreciated!

2. Originally Posted by dolphin1384
In dealing with metal surfaces that undergo oxidation, the thickness of the oxide film has been found to increase exponentially with time, such that d=dmax (1-e^(-kt)), t>2000 where d=thickness of oxide film and t=time.
This expression is the result of integrating an ordinary differential equation.

I'm trying to derive the Ordinary differential equation and the associated initial condition needed that produces d=dmax (1-e^(-kt))

Any help for how to approach this is much appreciated!
If:

$\displaystyle d(t)=d_{max} (1-e^{-kt})$

Then differentiating:

$\displaystyle d'(t)=d_{max} k e^{-kt}$

and $\displaystyle d(0)=0$.

CB