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 ≥ 0 is given by

M(t) = 250(1000 - t)(1 - 10^-30(1000 - t)¹⁰) 

and the volume of solution in the tank (in liters) 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?

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?

Transcribed Image Text:

lim C(t) t→1000