1) (2.3) Suppose a large mixing tank initially holds 300 gallons of water in whi
ID: 3167357 • Letter: 1
Question
1) (2.3) Suppose a large mixing tank initially holds 300 gallons of water in which 50 pounds of salt is dissolved. A brine solution is pumped into the tank at a rate of 3 gal/min with a concentration of 2 lb/gal. If the well-stirred solution is pumped out at the faster rate of 3.5 gal/min, set up an initial value problem and find the amount of salt in the tank at time t, A(t) dy 2) (2.4) Explain why the initial-value problem-=-cos(y): y(1) = has a unique solution. For that solution, find the equation of the tangent line when = 1.Explanation / Answer
1)
dA/dt = (rate)in (concentration)in -(rate)out (concentration)out
dA/dt = (3 gal/min)(2 lb/gal) - (3.5 gal/min) A / V, where V = 300 gal + (3 gal/min- 3.5 gal/min) t
A has units of lbs of salt.
dA/dt = 6 - 3.5A / [300 -0.5t ]
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