A large tank is filled to capacity with 500 gallons of pure water. Brine (a mixture of salt and water) containing 2 pounds of salt per gallon is pumped into the tank at a rate of 5 gallons per minute. The well-mixed solution is pumped out at a rate of 10 gallons per minute. Find the number

of pounds of salt in the tank at time

.

OK. I know that the rate at which the amount of salt is changing inside the tank with respect to time -

- is simply the net rate of the amount being pumped in and the amount being pumped out, that is

.

Now,

and

**I think** that

Assuming my

is correct, this would imply the DE

which is linear with the integrating factor

.

So, I have

Am I on the right track?