A large tank holds 3 0 0 gallons of water, and 5 0 pounds of salt is added to it to create a brine. A
A large tank holds gallons of water, and pounds of salt is added to it to create a brine. A concentration of brine that is pounds per gallon is pumped into the tank at a rate of gallons per minute. The solution is then mixed and pumped out of the tank at a rate of gallons per minute to maintain the total gallons of water.
Find an equation for the number of pounds of salt in the container at any time
a Find the concentration rate in and rate out of salt
b The rate of change in salt per minute is equal to Set up the first order differential equation and put it in standard form
c Solve the differential equation
d Apply the initial condition,
e How many pounds of salt will be in the tank after minutes? minutes?
f Using limits find the maximum number of pounds of salt in the tank.
