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Consider a linear growth process with immigration rate k where ?n = n? + k and µn = nµ
i. Write down the di?erence – di?erential equation for this process.
i. Show that M(t) = E{X(t)} for this process satis?es the di?erential equation M0(t) = (??µ)M(t) + k i.
Hence show that with initial condition M(0) = i if X(0) = i, Then M(t) = k ??µ{e(??µ)t ?1}+ ie(??µ)t, ? 6= µ