Drug Metabolism The rate at which a drug is absorbed into the bloodstream is modeled by the first-order differential equation:

where $\displaystyle a$ and $\displaystyle b$ are positive constants and $\displaystyle C(t)$ denotes the concentration of the drug in the bloodstream at time . Assume no drug is initially present in the bloodstream.

Find a formula for $\displaystyle C(t)$. You may need to use $\displaystyle a$ and $\displaystyle b$ in your answer.

*I think it may be the constants a and b, but something's throwing me off on how to do this. So far I've tried:*
$\displaystyle dC/dt = a-bC(t)$

$\displaystyle dC/dt -C(t)= a$

*And then I'm guessing I need to use an integrating factor? Or am I just completely wrong here. Any help is greatly appreciated!*