A raindrop of initial mass \(m_0\) is dropped from rest at time \(t = 0\) in a mist-filled atmosphere. As it falls under the influence of gravity, it absorbs stationary water droplets such that its mass increases at a rate \(\dfrac{dm}{dt} = b m\), where \(b\) is a positive constant. Assuming air resistance is negligible compared to the force required to accelerate the absorbed mist, which of the following expressions gives the speed \(v(t)\) of the raindrop as a function of time \(t\)?