Jose is studying a new population of fungi in the Quatretonda mountain range (Valencia). He observes that the rate at which the population grows is proportional to the product of the population at that moment and the difference between a certain stable population M and the population at that moment (follows a logistic model). Initially, he knows that the sample size is 3 kg and it grows at a rate of 2 kg per day. Some time later he notices that when the population is 6 kg it is growing at a rate of 3 kg per day. At what time does the population reach its maximum growth speed?