Many experiments are performed sequentially. Common practice is to randomize the order of the observations of the chosen design in order to minimize the possible impact of lurking variables. A lot of research has also been devoted to an alternative approach of designing experiments that benefits from taking into account available information about a time trend in the mean of the response. However, time trends can affect not just the mean but also the variance of the response. When the mean and the variance are related, as they are for some members of the exponential family of distributions, the trends to the mean and the variance are also related. We construct D-optimum experimental designs attuned for time trends in these cases that have not been studied before.