# Calculus

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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???

• Calculus -

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)

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