Salt Mixture Problem (First-Order Linear ODE Problem)
I just want to verify my work... Hopefully I was right:
A tank initially contains 100 gallons of brine in which 50 lbs. of salt are dissolved. A brine containing 2 lbs/gal of salt runs into the tank at the rate of 5 gal/min. The mixture is kept uniform by stirring and flows out of the tank at 4 gal/min.
IN: 2 lbs/gal AT: 5 gal/min
OUT: 4 gal/min
a) At what rate (lbs/min) does the salt enter the container at time t?
b) What is the volume of brine in the tank at time t?
c) At what rate (lbs/min) does salt leave the tank at time t?
d) Write and solve initial value problem.
e) Find the concentration of salt in the tank at 25 minutes after process starts.