Application of Differential Equations.
A 25% nitric acid solution flows at a rate of 6 litres/min into a large tank. Initially, the tank holds 200 litres of 5% nitric acid solution. The solution inside the tank is kept well stirred and flows out of the tank at a rate of 8 litres/min.
(a) If x(t) is the amount (in litres) of nitric acid in the tank after t minutes, prove that
Okay .. I have been trying to do it, I'm close to the answer but .. not getting there. Please help me out :)?
I know that
(Inflow Rate x Concentration) - (Outflow Rate) x
v(t) is the amount of solution in the tank at any minute which is defined as,
v(t) = 200 - (Inflow Rate - Outflow Rate)(t)
v(t) = 200 - 2t
so putting that back up to the dx/dt equation..
(6 x 25%) - 8 x
Hmm, I don't know what went wrong.
Anyway, does it matter that they told us that there was 5% of the nitric acid in the solution? Or can I just ignore that?