  Cells maintain a stable size as they grow and divide. Inspired by the
available experimental data, most proposed models for size homeostasis assume
size control mechanisms that act on a timescale of one generation. Such
mechanisms lead to short-lived autocorrelations in size fluctuations that decay
within less than two generations. However, recent evidence from comparing
sister lineages suggests that correlations in size fluctuations can persist for
many generations. Here we develop a minimal model that explains these seemingly
contradictory results. Our model proposes that different environments result in
different control parameters, leading to distinct inheritance patterns.
Multigenerational memory is revealed in constant environments but obscured when
averaging over many different environments. Inferring the parameters of our
model from {\it Escherichia coli} size data in microfluidic experiments, we
recapitulate the observed statistics. Our work elucidates the impact of the
environment on cell homeostasis and growth and division dynamics.
