Can this be turned into a differential equation? Recursive diffy Q?

[DrummingAtom]

Let's say you have a loss of 3% of the current energy on a device for every time is gets turned on. It starts at a 100% energy.

The only way I could think of it is a recursive function. Here's what I came up:

E(t) = E_t - .03*E_t-1

E(0) = 1

E(1) = 1 - .03*E₀

E(2) = E₁ - .03*E₁

...

Where E = Energy and t = each time turned on.

I feel like the solution should be something close to E^-.03t but it's not. I know the recursive function describes it exactly but I have to wonder if it's even possible to turn this into a differential equation?

Thanks.

 

[Skrew]

I don't think so considering you are look at specifc steps(each time you turn it on and off) and not a continuous interval..

 

[Office_Shredder]

Let me propose an alternative recursive formula (it should be obvious why this is the same)
E₁ = .97 E₀=.97
E₂ = .97 E₁=.97²

 

[TylerH]

I don't know anything about them, but this looks like a delay differential equation. http://en.wikipedia.org/wiki/Delay_differential_equation