or or y 200 50 e y 200 50 Therefore 40 e 1 50 40 ERT 40 loge Here the equation 4 gives the time t at which the salt in tank is y kg Step 4 Since e 40 is always positive from 3 we conclude that y 200 at all times Thus the minimum amount of salt content in the tank is 200 kg publishe 3 Also from 4 we conclude that t 0 if and only if 0 y 200 50 i e if and only if 200 y 250 i e the amount of salt content in the tank after the start of inflow and outflow of the brine is between 200 kg and 250 kg Rationalised 2023 24 4 Limitations of Mathematical Modelling Till today many mathematical models have been developed and applied successfully to understand and get an insight into thousands of situations Some of the subjects like mathematical physics mathematical economics operations research bio mathematics etc are almost synonymous with mathematical modelling But there are still a large number of situations which are yet to be modelled The reason behind this is that either the situation are found to be very complex or the mathematical models formed are mathematically intractable MATHEMATICAL MODELLING 207 The development of the powerful computers and super computers has enabled us to mathematically model a large number of situations even complex situations Due to these fast and advanced computers it has been possible to prepare more realistic models which can obtain better agreements with observations However we do not have good guidelines for choosing various parameters variables and also for estimating the values of these parameters variables used in a mathematical model Infact we can prepare reasonably accurate models to fit any data by choosing five or six parameters variables We require a minimal number of parameters variables to be able to estimate them accurately Mathematical modelling of large or complex situations has its own special problems These type of situations usually occur in the study of world models of environment oceanography pollution control etc Mathematical modellers from all disciplines mathematics computer science physics engineering social sciences are involved in meeting these challenges with courage