posted by Hannah on .
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???
The third equation does not follow from the second.
This looks like a differential equation they want you to solve.
What you need to do is integrate both sides of
dP/(P-a) = k dt
ln (P-a) = kt + constant
C e^(kt) = P-a
P = a + C e^(kt)
C is an arbitrary constant that you will have to determine from an initial condition.
check: dP/dt = k C e^(kt) = k (P-a)