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I seem to be having a hard time understanding the growth function. If I begin with

$x(t)=x(0)e^{-\lambda t}$

I can work backwards until I reach

$x'(t) = -\lambda x(t)$

Which is telling me that the rate of growth is the current amount times some constant. For some reason, my brain has a hard time making sense of that. Can someone explain that idea to me?

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