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

1. Apr 29, 2012

### 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) = Et - .03*Et-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.

2. Apr 30, 2012

### 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..

3. Apr 30, 2012

### Office_Shredder

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

4. Apr 30, 2012