Hi The kt function describes the effect of time on mortality. As this can only be observed for historical data, some assumption has to be made to project it into the future, but we are free to choose our method. In this question a straight line model for kt has been used. There is no single correct method for choosing the model for kt, which is why in the question this is presented as an assumption, rather than an output of the model. This is always the case with Lee-Carter. Hope this helps, Dave
