1 What is the concentration of our solution in the tank init

1. What is the concentration of our solution in the tank initially?

2. Find the amount of salt in the tank after 1 hours.

3.Find the concentration of salt in the solution in the tank as time approaches infinity

Solution

s/dt = 6/25 - s/125 ........ salt/time = rate of salt in - rate of salt out
d/dt [ s e^(t/125) ] = 6/25 e^(t/125)
s e^(t/125) = 6/25 e^(t/125) dt
s e^(t/125) = 30 e^(t/125) + C
... s[0] = 60 C = 30
s = 30 (1 + e^(-t/125))
s[240] = 30 (1 + e^(-240/125)) 34.4 kg .... note that 4 hrs = 240 min
lim(t ) 30 (1 + e^(-t/125)) = 30

Answer (a): 60/1000 = 0.06 kg/L
Answer (b): 34.4 kg
Answer (c): 30/1000 = 0.03 kg/L