Question

Suppose that a large mixing tank initially holds 500 gallons of water in which 60 pounds of salt have been dissolved. Pure water is pumped into the tank at a rate of 5 gal/min, and when the solution is well stirred, it is then pumped out at the same rate. Determine a differential equation for the amount of salt A(t) in the tank at time t > 0. What is A(0)

Answer 1

The answer is "
`(dA)/(dt)+ (A)/(100)=0\ \ and \ \A(0)=60`"

Explanation:

`A(0)=60\\\\ (dA)/(dt)=Rin-Rout\\\\Rin=0\\\\Rout=(A(t))/(500) * (5)\\\\ =(A)/(100)\\\\ so,\\\\(dA)/(dt)=Rin-Rout\\\\(dA)/(dt)=0- (A)/(100)\\\\(dA)/(dt)+ (A)/(100)=0\\\\A(0)=60`