Need help in solving this problem. Section is under limits at infinity, horizontal asymptotes...(a) A tank contains 5000L of pure water. Brine that contains 30g of salt per liter of water is pumped into the tank at a rate of 25L/min. Show that the concentration of salt after t minutes (in grams per liter) is
C(t)+ 30t/200+t
(b) what happens to the concentration as t--> infinity?

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Answer 1

Answer: (a) you can show the concentration by:

amount of salt / amount of water

amount of salt

= 30g / L

= [ 30 * 25g ] / [ 25L ] , 25L = 1 min

= [ 30 * 25g ] / min

amount of water

= 5000 + 25t

[ 30 * 25t ] / [ 5000 + 25t ]

= [ 30 * 25t ] / 25*[ 200 + t ]

= 30t / [ 200 + t ] yeah

(b)

lim t->∞ [ 30t / ( 200 + t ) ]

= lim t->∞ [ ( (1 / t) * 30t ) / ( (1 / t) * ( 200 + t ) ) ]

= lim t->∞ [ 30 / ( (200 / t) + 1 ) ]

= 30 / ( (200 / ∞) + 1 )

= 30 / 1

= 30

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