Question 4

Suppose we have a 400 liter tank. Suppose 8 litres per minute of salt water (brine) flows into the tank

at the top and then flows out of the tank at the bottom. Assume for simplicity that the salt water in the

tank is stirred so that its concentration is uniform in the tank. Let S(t) be the amount of salt, in grams,

in the tank at time t minutes. Suppose the salt water flowing into the tank has concentration 100 grams

per liter.

Find the differential equation to model the change in S(t).

Assuming there is no salt in the tank at time t=0 solve the differential equation using Maple.

What is S( ∞ )? That is, how much salt is in the tank after a long time?

Now graph S(t) for a suitable domain.