Afarmer has a mixing tank of capacity 1200 liters which she half-filled with pure, fresh water. she pumps into the tank a concentrated liquid fertilizer (clf) at rate 3 liters/minute, containing 1/3 ∼ 0.333 kilo/liter of nitrate (a salt of nitric acid), aiming at getting a right concentration 0.11 kilo/liter for the type of soil she has in her field.
unfortunately, the tank is leaking: when the farmer checks it after 90 min (that is, 1.5 hr) she finds the tank containing only 330 liters of solution. assume the leak is at the bottom of the tank. then: (a) determine the leakage in liters/minute. (b) in what time would the tank become empty? what is (c) the amount n(t) and (d) the concentration c(t) of nitrate in the tank at the time the farmer checked it? write the ivp for n(t) which you use for solving (c). (e) how much of the clf in liters has been pumped in by the time she checked the tank?
in absence of leakage: (f) when would c(t) equal the right level 0.11, (g) how much of solution should be in the tank at that time?