Brine (saltwater) is entering a 25 m3 tank at ?ow rate of 0.25 m3 /min and at a

Question

Brine (saltwater) is entering a 25 m3 tank at ?ow rate of 0.25 m3 /min and at a concentration of 6 g/m3 . The uniformly mixed solution exits the tank at a rate of 0.25 m3 /min. Assume that initially there are 15 m3 of solution in the tank at a concentration of 3 g/m3.

(a) State an IVP that is satis?ed byA(t), the amount of salt in grams in the tank at time t.

(b) What will happen to the amount of salt in the tank ast ? ?? Why?

(c) Plot a direction ?eld for the IVP stated in (a), including a plot of the solution.

(d) At exactly what time will there be 75 g of salt present in the tank?

Please show work. Thanks!

Explanation / Answer

.salt entering = .25*6 per min = 1.5

salt exiting = .25*y per min where y is concentration

A(T) = 1.5t - .25 *y*t +(15*3) -----------------(1)

y= (.25*6+15*3) /(15+.25) = 3.04

there fore A(T) = 1.5T- 0.76T+45 = 0.74T+45

b and c parts are not clear

d)

75 = 0.74T +45

.74T =30

T= 40.54 MIN

HENCE TANK WILL CONTAIN 75 GM WHEN T= 40.54 MINUTES

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