In the development of a fermentation medium, a characteristic pattern of improvement is seen. When the maximum (or minimum) values to date of various indicator variables, for example the volumetric productivity or medium cost per unit product formed, are plotted versus the number of media tested, an exponential increase (or decrease) is seen until a plateau is reached. These plots are very useful to indicate the number of media that need to be tested before a new strategy in medium optimization must be sought. This new strategy may be to test a different set of substrates, to try different concentration regimes of various substrates, or to try a different mathematical optimization procedure. As a result these plots and models are helpful in decreasing the time and effort involved in medium design. The medium design kinetic plots for the production of polyunsaturated fatty acids (PUFA) by four different filamentous fungi are presented.