Solve: dA/dt = -10A, A(0) = 5

Question

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I tried getting A by itself:

A = -1/10 * dA/dt
A(0) = 5 = -1/10 * dA/dt

but I'm somewhat sure that's wrong; so integrating I get:

int(dA/dt) = int(-10A)
A = -5A^2

which doesn't make sense to me intuitively since the same variable is on both sides. I'm a bit confused, any help is appreciated.

Answer 1

A = -1/10 * dA/dt
dA/A=-10dt
lnA=-10t+C
when t=0, A=5
ln5=C
LnA=-10t+ln5

Answer 2

ah, I see! thank you