A mixing tank A 500-liter (L) tank is filled with pure water. Attime t = 0, a salt solution begins flowing into the tank at a rate of5 L/min. At the same time, the (fully mixed) solution flows outof the tank at a rate of 5.5 L/min. The mass of salt in grams in thetank at any time t Ú 0 is given byM(t) = 250(1000 - t)(1 - 10-30(1000 - t)10)and the volume of solution in the tank is given byV(t) = 500 - 0.5t.a. Graph the mass function and verify that M(0) = 0.b. Graph the volume function and verify that the tank is emptywhen t = 1000 min.c. The concentration of the salt solution in the tank (in g/L) isgiven by C(t) = M(t)>V(t). Graph the concentration functionand comment on its properties. Specifically, what are C(0)and lim t-S1000- C(t)?d. Find the rate of change of the mass M′(t), for 0 <, t < 1000.e. Find the rate of change of the concentration C′(t), for0 < t < 1000.f. For what times is the concentration of the solution increasing?Decreasing?
A mixing tank A 500-liter (L) tank is filled with pure water. At
time t = 0, a salt solution begins flowing into the tank at a rate of
5 L/min. At the same time, the (fully mixed) solution flows out
of the tank at a rate of 5.5 L/min. The mass of salt in grams in the
tank at any time t Ú 0 is given by
M(t) = 250(1000 - t)(1 - 10-30(1000 - t)10)
and the volume of solution in the tank is given by
V(t) = 500 - 0.5t.
a. Graph the mass function and verify that M(0) = 0.
b. Graph the volume function and verify that the tank is empty
when t = 1000 min.
c. The concentration of the salt solution in the tank (in g/L) is
given by C(t) = M(t)>V(t). Graph the concentration function
and comment on its properties. Specifically, what are C(0)
and lim t-S1000- C(t)?
d. Find the rate of change of the mass M′(t), for 0 <, t < 1000.
e. Find the rate of change of the concentration C′(t), for
0 < t < 1000.
f. For what times is the concentration of the solution increasing?
Decreasing?
Step by step
Solved in 3 steps with 3 images
