Hopefully this is the right forum for this. I'm going over a Math Modeling book which is dealing with drug dosage modeling and i'm having trouble figuring out how they reached the following conclusion.

If we assume that C(0) is the concentration at t = 0, then we have the model:

dC / dt = -k * C

implies

C(t) = C(0) * e^(-k * t)

I've taken Calc. 3, so I feel like I should have some idea of what's going on here, but I can't remember. My idea:

dC / dt = -k * C

dC = -k * C * dt

integral(1)dC = integral(-k * C)dt

c = -k * c * t + constant

1 = -k * t + constant

-k * t = constant.

Which, is a far cry from what the book has come up with. Could someone give me an idea of what's going on here?