Suppose a tank initially contains 50 gallons of water. Then water containing a concentration of three grams per gallon of salt begins to enter the tank at a rate of 6 gallons per hour. The water flows out of the tank mixed at a rate of 5 gallons per hour. The tank can hold 100 gallons of water. Please use a constant other than c because C is concentration in this context and show each step with work. Thank you!
(a) It should be clear that the volume of water in the tank is increasing as time passes. At what time 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 onl model the situation at hand up until the t-value you found in (a).) (c) Let ty 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 0ã1ã1, . Use this to compute the amount and concentration of salt in the tank at the moment that it fills up.
