dP/dt = k(P-a)

dP/dt = kP-ka

dP/P = k-ka

is this right so far? was i supposed to distribute??? what do i need to do next???

Yes, you're on the right track so far. To solve the equation, you can separate variables and integrate both sides with respect to their respective variables.

Starting with:

dP/P = k - ka

You can multiply both sides by dt to separate the variables:

dP = (k - ka) dt

Now, you can integrate both sides. Integrating the left side with respect to P and the right side with respect to t:

∫dP = ∫(k - ka) dt

The integral of dP with respect to P is simply P:

P = ∫(k - ka) dt

Integrating (k - ka) dt with respect to t will give you:

P = k * t - ka * t + C

where C is the constant of integration.

Therefore, the general solution to the equation is:

P = k * t - ka * t + C

To determine the value of the constant C, you will need an initial condition or boundary condition for P at a specific time (t) or given information about the problem. You can substitute the initial condition into the equation to find the specific value of C.

So, you need more information or an initial condition to find the exact solution.