A cylindrical tank contains 40 gal of brine solution containing 2 lb of salt per gallon. A salt solution of concentration 3 lb/gal flows into the tank at 4 gal/min.
a.)How much salt is in the tank at t=20 min if the well-stirred mixture flows out at 4 gal/min?
b.) How much salt is in the tank when time t approaches infinity?

a. is 114.6
b. kinda lost in the infinity part

Question

A cylindrical tank contains 40 gal of brine solution containing 2 lb of salt per gallon. A salt solution of concentration 3 lb/gal flows into the tank at 4 gal/min.
a.)How much salt is in the tank at t=20 min if the well-stirred mixture flows out at 4 gal/min? 
b.) How much salt is in the tank when time t approaches infinity? 

a. is 114.6
b. kinda lost in the infinity part

rational · Answer

$$x(t) = 120-40e^{-t/10}$$

rational · Answer

Did you get that as  solution ?

rational · Answer

As far as part b is concerned, you don't even need to know calculus. You can answer by observing that the concetration in the tank will reach the input concentration of 3 lb/gal if you wait long enough...

rational · Answer

Since the tank capacity is 40 gal, and the input concentration is 3 lb/gal, the amount of salt in the tank will approach 40*3 = 120 lb asymptotically

anonymous · Answer

Wow. Thanks man! Appreciate it.

rational · Answer

yw