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.(adsbygoogle = window.adsbygoogle || []).push({});

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*E_{0}

E(2) = E_{1}- .03*E_{1}

....

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.

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

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