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## Homework Statement

If f'(x) = -f(x) and f(1) = 1, then f(x) = ?

(A) [itex]\frac{1}{2}[/itex]e

^{-2x+2}.

(B) e

^{-x-1}.

(C) e

^{1-x}.

(D) e

^{-x}.

(E) -e

^{x}.

## Homework Equations

P(t) = P

_{0}e

^{kt}.

[itex]\frac{dP}{dt}[/itex] = kP.

## The Attempt at a Solution

I was thinking f(1) = t and 1 = P

_{0}, therefore:

P(1) = e

^{k}.

Then, I exponetiated both sides and got:

ln(P(1)) = k.

I'm probably going off in a completely different direction, but this is what I did so far.