 In this module which is the last module of fat batch culture kinetics in this module we will discuss about the change in product concentration during the fat batch as we are already discussed that part reported the fat batch culture kinetics in 1975 in detail. So as per described the product balance in fixed volume fat batch system. So we can say that the dp over dt is equal to qx. So change in product concentration with respect to change in time that is qp dot x. So this equation is basically that kind of the product base is directly associated with the biomass. As the biomass will increase then that have the effect on the change in product concentration. So by substituting here the x you can see here that if we put this dp over dt is equal to qp x in our previous equation in which we have a xt over that. So we have this equation because in previous module we discussed about our equation in which xt is equal to xa plus gy into that. So if we put the mu is equal to dp or js then we can have this equation. So if the product concentration is strictly growth related then product concentration will rise linearly as for the biomass. But however if the qp is constant then the rate of increase in product concentration will rise as growth rate decline. So at the time progress and x increase. So easily we can understand here that how the product quotient are rate of product formation effect by the x. So if the qp is related to the mu mean specific growth rate in a complex manner then the product concentration will vary according to the relationship. So in this picture you can see that there are two different relationships A and B. A deal with the variable volume and B deal with the fixed volume and these are both diagrams as modified by reported by the part 1979. So in this equation in this relationship you can see that so in variable volume so the p what is the line of that. So dotted line show that product that is associated with the biomass because in variable volume x remain constant mean the biomass concentration remain constant as well as the product concentration remain the constant. But in case of the fixed volume sometimes due to the fluctuation then the product concentration can vary but then it gradually have the effect on increase. But almost it remain constant when there is a relationship of that. But as concern in a fixed volume that there is a continuous increase in biomass as well as we can say that there is a linear relationship in the product concentration by the same way we can say that either that is growth related or not growth related. So in both cases in fixed volume we have a very increase or a linear relationship between the product formation or a rate of product formation during the fermentation process. So these two diagrams easily show us that what kind of the relationship in fixed volume and the variable volume with respect to those secretion become very toxic that have a very negative effect on the a mu which we called as specific growth rate. So in fixed volume when there is a constant increase in the toxic secretions by the organism itself that can have a very negative effect or a very difficult or can create a difficult situation in order to maintain mu is equal to D mean specific growth rate is equal to the dilution rate. So here we can see that there is no dilution rate when we talk about the fixed volume but we can see here that D instead of D we can use at the G. So the feeding strategy with respect to mu is very critical that also depend upon the secretion during the fat batch. So keep in view the fat batch then we will in the next module we will see that there is a continuous culture in which there will be a continuous harvesting of some fermentation along with the feeding to remain the volume constant.