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Mitscherlich's function is a well-known three-parameter non-linear regression function that quantifies the relation between a stimulus or a time variable and a response. It has many applications, in particular in the field of measurement reliability. Optimal designs for estimation of this function have been constructed only for normally distributed responses with homoscedastic variances. In this paper we generalize this literature to D-optimal designs for discrete and continuous responses having their distribution function in the exponential family. We also demonstrate that our D-optimal designs can be identical to and different from optimal designs for variance weighted linear regression. [ABSTRACT FROM AUTHOR]