  In this work, we study the shadow boundary curves of rotating time-dependent
black hole solutions which have well-defined Kerr and Vaidya limits. These
solutions are constructed by applying the Newman-Janis algorithm to a
spherically symmetric seed metric conformal to the Vaidya solution with a mass
function that is linear in Eddington-Finkelstein coordinates. Equipped with a
conformal Killing vector field, this class of solution exhibits separability of
null geodesics, thus allowing one to develop an analytic formula for the
boundary curve of its shadow. We find a simple power law describing the
dependence of the mean radius and asymmetry factor of the shadow on the
accretion rate. Applicability of our model to recent Event Horizon Telescope
observations of M87${}^*$ and Sgr A${}^*$ is also discussed.
