Salt water with a concentration of 0.2 pounds of salt per gallon flows into a la

Question

Salt water with a concentration of 0.2 pounds of salt per gallon flows into a large tank that initially contains 50 gallons of fresh water. (Hint: Refer to Section 3.6, pages 1 and 2 of our e-text for this type of problem if you need to).

Multiple Choice: If the flow rate of salt water into the tank is 4 gallons per minute, what is the volume V(t) of water and the amount A(t) of salt in the tank t minutes after the flow begins?

a. V(t) =50 +4t, A(t)=0.2t

b. V(t)=50+4t, A(t)=0.8t

c. V(t)=4t, A(t)=0.2t

d. V(t)= 4t, A(t)=0.8t

If salt concentration C(t) in the tank of water is defined as: C(t)= 0.8t/4t+50

Please show the work for this problem

Explanation / Answer

b. V(t)=50+4t, A(t)=0.8t

lim t->infinity C(t) = lim t->infinity 0.8t/(4t+50) = 0.8/(4+ 50/t) = 0.8/(4+0) = 0.2

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