As plastic production increases, so to do the threats from plastic pollution. Microplastics (defined as plastics <5 mm) are a subset of marine debris about which we know less than we do of larger debris items, though they are potentially ubiquitous in the marine environment. To quantify the distribution and change in microplastic densities through time, we sampled sediment cores from an estuary in Tasmania, Australia. We hypothesized that the type, distribution and abundance of microplastics observed would be associated with increasing plastic production, coastal population growth, and proximity to urban water outflows and local hydrodynamics. Sediments ranging from the year 1744 to 2004 were sub-sampled from each core. We observed microplastics in every sample, with greater plastic frequencies found in the upper (more recent) sediments. This time trend of microplastic accumulation matched that of global plastic production and coastal population growth. We observed that fibers were the most abundant type of microplastic in our samples. These fibers were present in sediments that settled prior to the presence of plastics in the environment. We propose a simple statistical model to estimate the level of contamination in our samples. We suggest that the current trend in the literature suggesting very high loads of fibers, particularly in remote locations such as the deep seafloor, may be largely due to contamination.