Use a letter other than C for undetermined constants since C is for Concentration in this context. Please show each step with work. Thank you!!
Suppose that a tank initially contains 50 gallons of pure water. Water containing a concentration of 3 grams per gallon of salt begins to enter the tank at a rate of 6 gallons per hour, while the well-stirred tank water fows othughapipe at a rate of 5 gallons per hour. Supposha the tank can hold (a) It should be clear that the volume of water in the tank is increasing as time passes. At what time 100 gallons of water. will the tank fill up? (b) Write down a differential equation which describes the amount X(t) of salt in the tank at any time t 2 0, together with an initial condition satisfied by X. (Note that your equation will only model the situation at hand up until the t-value you found in (a).) (c) Let t denote the time at which the tank becomes full (which you computed in (a). By solving the DE you wrote down in (b) and using the initial condition to find the undetermined constant, compute an exact formula for X(t) which is valid for 0 S t
