Fresh water is poured at a rate of 4 gallons per minute into a
tank A, which initially contains 100 gallons of water in which 40
lbs of salt are dissolved. The stirred mixture flows out of tank A
at a rate of 4 gallons per minute into a second tank B that
contains 100 gallons of fresh water. The mixture in tank B is
stirred and flows out at a rate of 4 gallons per minute.
a) Write down a differential equation and initial condition
which models the amount of salt in tank A.
b) Solve your differential equation in part a) to find the
amount of salt in tank A at any time.
c) What are the minimum, maximum and long-term values for the
amount of salt in tank A?
d) Write down a differential equation and initial condition that
models the amount of salt in tank B.
e) Solve your differential equation in part d) to find the
amount of salt in tank B at any time.
f) What are the minimum, maximum and long-term values for the
amount of salt in tank B?